[User]
Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:
[[26, -1, 16, 4, -12, 19, -23, -5, 18, 9],
 [0, -1, -24, -28, -30, 5, -6, 6, -30, -16],
 [0, 0, 9, -23, -26, 29, -22, -30, 5, 4],
 [0, 0, 0, -22, 3, 15, -17, -27, -1, 0],
 [0, 0, 0, 0, -28, -17, 29, -18, 14, 1],
 [0, 0, 0, 0, 0, 7, -15, -29, 9, -14],
 [0, 0, 0, 0, 0, 0, 29, -29, -29, -5],
 [0, 0, 0, 0, 0, 0, 0, -28, -23, -8],
 [0, 0, 0, 0, 0, 0, 0, 0, 8, -30],
 [0, 0, 0, 0, 0, 0, 0, 0, 0, 26]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute |A| for the matrix A =
[[-18, 6, 7, -7, -29, -9, -14, 5, -17, -21],
 [4, -6, -28, 16, 7, -14, -19, 23, 21, -7],
 [-2, 12, -6, 5, 27, 29, -5, 7, -30, -11],
 [24, -3, -15, 16, -14, 9, -3, 27, -19, -4],
 [23, 22, 11, 28, 16, -1, 10, 3, 6, -25],
 [-24, 1, 1, 22, -6, 2, 24, 27, -24, 21],
 [26, -19, -15, -15, 12, 22, 5, -18, -24, 5],
 [16, 20, -22, 1, -20, -23, 2, -8, -6, 25],
 [-23, 14, -9, 28, -27, 9, -28, -2, 10, -2],
 [3, 3, -3, -18, -16, 29, -8, 13, -5, -27]]
Round to the nearest integer, then take the result modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:
[[20, -30, 1, -6, -2, -24, 18, -28, -11, -11],
 [22, -1, 4, 4, 18, 8, -4, -5, -17, -14],
 [-13, 14, 21, -2, -11, 22, -4, -13, -27, -30],
 [19, -30, 27, -5, 14, -11, 21, -8, -21, 28],
 [-20, 10, 10, -26, 27, -30, -14, -9, 3, 25],
 [14, 10, -2, -27, -26, -20, 25, 20, -10, 4],
 [-19, -5, 20, -12, 14, 29, -24, 16, 24, -24],
 [-5, 9, -26, -10, -17, -27, -8, 11, -11, -16],
 [19, 21, 14, -2, -23, 10, 17, -12, 17, 8],
 [15, -3, 15, 26, -4, -27, 27, -16, 4, 6]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:
[[-21, -6, -11, 0, -27, 13, -8, -29, 25, -9],
 [20, 26, 6, -23, -24, -17, 25, 24, -28, 19],
 [-15, 24, -12, 20, -13, 21, -15, -23, 29, 2],
 [18, -19, 22, -20, -26, -4, -19, -14, -25, 2],
 [-26, 26, -3, -17, -26, 23, 25, 28, 2, 19],
 [17, 10, -12, -9, -26, 28, -29, -1, 16, 8],
 [-27, 2, -18, -11, 23, -24, -16, -8, -17, -8],
 [-12, 23, -2, 25, -11, -2, -7, -13, -21, 10],
 [26, -23, -5, -2, -21, -14, -29, -25, 27, -26],
 [-3, 10, -26, -13, -5, -11, 10, 18, -4, 18]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the value of det(A) where A =
[[27, -2, -10, -10, 9, -8, 25, -25, -9, 19],
 [0, 6, 14, 20, 23, -23, 10, 18, 4, 20],
 [0, 0, 18, -10, 20, -29, 9, -12, 8, -3],
 [0, 0, 0, -12, 25, 7, -3, -29, 7, 24],
 [0, 0, 0, 0, -9, -5, 18, 12, 5, 27],
 [0, 0, 0, 0, 0, 10, 5, 24, 29, 15],
 [0, 0, 0, 0, 0, 0, 25, 28, -3, -30],
 [0, 0, 0, 0, 0, 0, 0, -7, -15, 19],
 [0, 0, 0, 0, 0, 0, 0, 0, -19, 0],
 [0, 0, 0, 0, 0, 0, 0, 0, 0, 23]]
Round to the nearest integer, then give your answer as det(A) mod 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the value of det(A) where A =
[[-2, 8, 29, 3, 12, 14, -8, -26, -1, -25],
 [25, 27, 30, 15, 13, -27, -2, -8, -25, 1],
 [11, -13, -16, 9, 27, 1, -22, 6, -21, -11],
 [-25, 17, 25, 28, -28, 11, -20, 12, -14, 1],
 [-27, -27, -14, 10, -12, -26, 1, -9, 25, -25],
 [4, -9, -30, -11, -9, 17, 24, -20, -18, 28],
 [11, -28, -22, 29, -19, -8, -17, 2, -13, 18],
 [28, 10, -22, -8, -21, -12, 30, 16, -26, 16],
 [21, -8, -1, -6, -3, 3, 14, 25, 17, 16],
 [-6, -21, -17, 11, 26, 15, 27, -1, 24, 10]]
Round to the nearest integer, then give your answer as det(A) mod 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:
[[-17, 12, 14, 12, 13, 12, 14, 6, 20, -24],
 [12, -25, 20, -20, -26, 20, 6, 10, -7, -4],
 [14, 20, -8, 4, 0, 16, 8, -18, -12, -20],
 [12, -20, 4, 16, -18, 8, -14, -12, -6, -4],
 [13, -26, 0, -18, 4, 16, 14, -20, -5, 18],
 [12, 20, 16, 8, 16, 13, 18, 14, 3, 26],
 [14, 6, 8, -14, 14, 18, -18, -3, -18, -23],
 [6, 10, -18, -12, -20, 14, -3, 23, 8, -2],
 [20, -7, -12, -6, -5, 3, -18, 8, -12, -3],
 [-24, -4, -20, -4, 18, 26, -23, -2, -3, 5]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:
[[-19, -29, 12, -17, -9, 0, -8, 17, -11, 30],
 [7, 24, -27, -16, -7, -6, -30, -24, 26, 0],
 [-19, 11, -26, 13, 19, 11, 7, 29, -19, 8],
 [-13, -29, -21, -16, -1, 13, 27, -14, -27, -24],
 [10, 0, 20, 29, 28, 24, 8, 24, 3, -25],
 [19, 7, 14, 27, 20, 3, 13, -16, -17, -25],
 [19, 6, 19, 1, -28, -28, -9, -9, -21, 20],
 [-28, 30, -19, -2, 17, -14, -24, -18, 25, -29],
 [-27, -21, 8, -7, -14, 21, -25, -12, -26, 1],
 [-21, -22, -4, -18, -12, -10, -7, 7, -27, -7]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:
[[6, -11, 8, -7, 17, -11, -30, -30, -14, 28],
 [-30, 22, 21, 14, -1, 10, 16, -28, 15, 24],
 [-20, -7, -9, 13, 14, -5, -18, -30, -7, -21],
 [4, -7, -3, 5, -15, 9, -15, 28, -14, 20],
 [23, -16, -15, -16, 26, 3, -20, -30, -16, -5],
 [20, -27, 12, -26, 4, -18, -21, -20, -13, 3],
 [8, 10, 11, 19, -8, -24, 28, 8, -28, -19],
 [-24, 18, -5, 2, 6, 17, -16, -29, 10, -24],
 [1, -27, -11, 19, 22, 5, 1, -3, -18, -30],
 [29, 25, 4, 17, -1, 23, 5, 26, 24, -6]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the value of det(A) where A =
[[-24, -22, -18, 27, -28, 4, 2, -10, 0, 21],
 [0, 1, 26, 4, -16, 25, 1, -25, 14, -10],
 [0, 0, 21, -12, 2, -3, 0, -10, 23, 3],
 [0, 0, 0, 12, -16, -25, 21, -22, 6, -11],
 [0, 0, 0, 0, -3, 30, 24, 20, -22, 1],
 [0, 0, 0, 0, 0, -17, -3, 27, -7, 30],
 [0, 0, 0, 0, 0, 0, -4, 27, -12, -7],
 [0, 0, 0, 0, 0, 0, 0, 5, 11, -2],
 [0, 0, 0, 0, 0, 0, 0, 0, -21, -6],
 [0, 0, 0, 0, 0, 0, 0, 0, 0, -23]]
Round to the nearest integer, then give your answer as det(A) mod 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the value of det(A) where A =
[[4, -4, -6, -13, 23, -30, 30, 17, 8, -28],
 [24, -27, 10, 6, 20, -16, -23, 7, 19, -12],
 [25, 16, -5, 8, -21, 7, -17, 18, 10, -12],
 [-1, -26, 24, 0, -24, -12, 0, 21, 27, 8],
 [-7, 3, 26, -8, 17, 14, 9, -25, 7, 10],
 [5, -4, -20, -26, 26, -14, 21, -24, -4, 16],
 [26, -16, 15, -18, -20, 29, 14, -5, -9, -3],
 [-7, -2, -22, 11, -27, 18, 15, 25, -13, 12],
 [-15, 2, -2, 8, 29, -21, -22, 28, 0, -3],
 [29, 26, -28, 23, 24, -17, 27, -6, -16, -29]]
Round to the nearest integer, then give your answer as det(A) mod 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the value of det(A) where A =
[[-7, -17, 17, -24, 5, 19, -7, -4, 6, 7],
 [-1, -4, 8, -16, -5, -30, 25, -27, -2, 26],
 [-30, 12, 19, 15, -9, -20, -21, 28, -14, 5],
 [25, 16, -5, 17, -10, -18, -22, -20, -20, -25],
 [-30, 23, -25, -18, -9, 25, 0, -9, 6, 16],
 [-4, 19, 21, -17, 16, 27, -26, 27, 5, 1],
 [3, -24, 11, 17, -21, 19, -14, -1, -10, 29],
 [-18, -30, -30, 16, 2, 7, -6, -5, -18, 28],
 [-3, 2, 6, 10, -1, 26, 18, 17, -23, 18],
 [16, 25, -30, -19, -26, -7, -25, -6, -30, -6]]
Round to the nearest integer, then give your answer as det(A) mod 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:
[[0, -6, 5, 6, 14, 3, 18, -12, -22, 18],
 [-6, 16, 21, 6, -15, -24, 20, 16, 8, 5],
 [5, 21, -9, -5, -4, 24, 24, -7, 2, -20],
 [6, 6, -5, 18, -22, 2, 12, 4, 11, 2],
 [14, -15, -4, -22, 0, -11, 9, 10, 24, -6],
 [3, -24, 24, 2, -11, -21, 4, -13, -13, -5],
 [18, 20, 24, 12, 9, 4, -12, 8, 6, -1],
 [-12, 16, -7, 4, 10, -13, 8, -28, 30, 30],
 [-22, 8, 2, 11, 24, -13, 6, 30, -13, -11],
 [18, 5, -20, 2, -6, -5, -1, 30, -11, -16]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the value of det(A) where A =
[[21, -16, -6, -8, 6, 22, -5, 6, 6, 8],
 [-16, -30, -18, -6, 22, -6, -4, -10, -6, -20],
 [-6, -18, 14, -3, 5, -14, -14, -10, -1, 6],
 [-8, -6, -3, 11, -14, -23, 16, 7, -15, -1],
 [6, 22, 5, -14, 19, -23, 16, -13, -6, -6],
 [22, -6, -14, -23, -23, -24, 4, -20, 8, -6],
 [-5, -4, -14, 16, 16, 4, 8, -12, -14, 18],
 [6, -10, -10, 7, -13, -20, -12, 15, -2, 8],
 [6, -6, -1, -15, -6, 8, -14, -2, -27, -12],
 [8, -20, 6, -1, -6, -6, 18, 8, -12, -14]]
Round to the nearest integer, then give your answer as det(A) mod 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:
[[-4, 12, -18, -14, 0, 22, -17, 16, -4, -24],
 [12, 30, 17, 0, -18, -8, -11, 4, -5, 17],
 [-18, 17, 6, -21, 8, 0, 8, -15, 6, -12],
 [-14, 0, -21, 14, 14, -20, 12, 20, -4, -18],
 [0, -18, 8, 14, -7, -10, 2, -10, -26, -18],
 [22, -8, 0, -20, -10, 13, -11, -7, -20, -22],
 [-17, -11, 8, 12, 2, -11, -23, 15, -12, -16],
 [16, 4, -15, 20, -10, -7, 15, -17, 4, -2],
 [-4, -5, 6, -4, -26, -20, -12, 4, 13, -25],
 [-24, 17, -12, -18, -18, -22, -16, -2, -25, 26]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the determinant of the matrix:
[[22, -22, 28, 24, -22, -19, 24, 10, -16, -29],
 [-20, -20, -23, 24, 1, -25, 22, -11, 8, 4],
 [-23, 19, 18, 12, 3, 26, 22, 28, 25, -12],
 [-24, 0, -13, 9, -17, 8, 29, 22, 29, 28],
 [5, -14, 6, 13, -22, 27, -11, 14, 26, -3],
 [19, -11, 10, 5, 22, -4, -23, 1, -30, -14],
 [26, -22, -11, 14, 1, -29, 1, 14, -22, -1],
 [-11, 7, 29, -30, 29, 26, -26, 4, 5, -30],
 [-17, -22, -1, -7, -27, 19, -17, -6, -27, -6],
 [-21, 4, 24, -24, 11, -18, -27, 19, 12, 26]]? Round to the nearest integer, then express your answer modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute |A| for the matrix A =
[[-17, -14, -1, -6, 12, 14, -22, 20, -2, -2],
 [-14, -10, 8, 6, 8, 28, 24, 22, 13, -10],
 [-1, 8, 3, 12, -22, 2, 10, -2, -2, -4],
 [-6, 6, 12, -13, 0, 25, -6, -14, 0, -15],
 [12, 8, -22, 0, 17, -2, 1, -2, -4, -4],
 [14, 28, 2, 25, -2, 25, -20, -10, 23, 14],
 [-22, 24, 10, -6, 1, -20, 26, 20, -6, -4],
 [20, 22, -2, -14, -2, -10, 20, -11, -3, 12],
 [-2, 13, -2, 0, -4, 23, -6, -3, -13, 20],
 [-2, -10, -4, -15, -4, 14, -4, 12, 20, 14]]
Round to the nearest integer, then take the result modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:
[[-10, 15, -1, -21, -5, -4, -23, 8, -23, 29],
 [-23, 24, 3, 28, -15, 10, -18, -8, -19, -4],
 [-9, 1, 26, 30, 18, -4, -29, 14, 2, -5],
 [-3, -12, 12, -26, 2, -11, -1, 14, -23, 7],
 [30, -14, 13, -30, -28, 15, -5, 0, -23, 12],
 [28, 15, -23, 30, 4, 8, -3, 20, -27, 26],
 [-15, -18, -11, 20, -26, 24, 6, -11, -7, 5],
 [3, 27, 14, 17, 23, 3, -12, -14, -26, -6],
 [-13, 29, 24, 22, 19, -23, -4, -16, 14, -18],
 [-15, -9, -11, -18, -11, -29, 4, 16, 24, -12]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:
[[-29, -14, 7, -6, 18, -4, -17, -12, -10, 22],
 [-14, -7, 16, -14, 18, 4, -14, 22, -3, -5],
 [7, 16, 19, -27, -12, -16, 2, 14, -23, -6],
 [-6, -14, -27, -22, -13, -20, -9, 4, -26, 9],
 [18, 18, -12, -13, -11, -15, -10, 11, -13, 2],
 [-4, 4, -16, -20, -15, -22, -21, 10, -16, 4],
 [-17, -14, 2, -9, -10, -21, 23, 6, -26, 14],
 [-12, 22, 14, 4, 11, 10, 6, -3, 16, -14],
 [-10, -3, -23, -26, -13, -16, -26, 16, 26, 11],
 [22, -5, -6, 9, 2, 4, 14, -14, 11, -30]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the determinant of the matrix:
[[-9, -16, -5, -13, 17, -22, -30, 12, -22, -8],
 [12, 14, 27, -29, -17, 7, 9, -13, -15, 22],
 [-2, 13, -20, -25, -28, -17, 29, -29, 1, 0],
 [-20, -9, -28, 19, 0, 2, -7, -30, 13, -16],
 [6, -4, 7, 17, -4, 13, -19, -28, -1, 1],
 [-8, -29, -24, 3, 1, 22, 8, 1, 12, 12],
 [-17, -28, 15, 1, 12, 5, -14, 17, -28, 26],
 [-21, 22, 16, 9, -13, -28, 8, -21, 21, -22],
 [15, 24, 15, -20, 29, 2, 5, -5, -4, 7],
 [-9, -5, -9, -26, 4, -29, 4, -22, 20, 20]]? Round to the nearest integer, then express your answer modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute |A| for the matrix A =
[[-23, -4, -21, -17, 15, 28, 21, 23, -20, -25],
 [-10, 2, -12, 8, -7, -13, 4, 21, 12, 6],
 [-12, 22, -7, 25, 3, -9, -27, 26, -21, -29],
 [-23, 2, 28, 7, 12, 28, -3, -21, 14, -30],
 [3, -28, -22, -26, 11, -21, -19, -13, 27, -10],
 [-10, -30, -28, -26, -6, 27, 18, -23, -14, -22],
 [1, -25, 18, 9, -10, -24, -24, 16, 8, 23],
 [-4, -23, -22, -3, -16, -29, -24, 16, -13, -9],
 [19, -21, 23, 19, 2, -24, -28, -17, 13, 15],
 [30, 5, -18, -15, -15, 23, -26, 21, -6, 7]]
Round to the nearest integer, then take the result modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the value of det(A) where A =
[[9, -4, 12, -6, 10, -12, -19, 18, -22, -12],
 [-4, -14, 12, 8, -9, 9, -7, -21, 0, -24],
 [12, 12, 25, 19, -6, -26, -2, 4, 13, 8],
 [-6, 8, 19, 1, 22, -18, 0, -12, -4, 9],
 [10, -9, -6, 22, -4, -16, 14, -2, -4, 8],
 [-12, 9, -26, -18, -16, 23, -1, -1, -18, -12],
 [-19, -7, -2, 0, 14, -1, 30, 13, -8, -4],
 [18, -21, 4, -12, -2, -1, 13, -16, -3, -14],
 [-22, 0, 13, -4, -4, -18, -8, -3, 5, 8],
 [-12, -24, 8, 9, 8, -12, -4, -14, 8, 30]]
Round to the nearest integer, then give your answer as det(A) mod 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:
[[-26, -20, 16, 12, -6, -6, -7, 24, 20, 16],
 [-20, 19, 3, 2, 0, 20, -14, 14, -2, 14],
 [16, 3, 8, -4, 22, -18, 0, 6, -10, 4],
 [12, 2, -4, 30, 18, 19, -3, 14, -11, 4],
 [-6, 0, 22, 18, 22, 16, -8, -9, -4, 6],
 [-6, 20, -18, 19, 16, -27, 1, 24, 6, 15],
 [-7, -14, 0, -3, -8, 1, 14, -2, 9, 12],
 [24, 14, 6, 14, -9, 24, -2, -27, -18, 19],
 [20, -2, -10, -11, -4, 6, 9, -18, 14, -2],
 [16, 14, 4, 4, 6, 15, 12, 19, -2, 23]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the determinant of the matrix:
[[-16, -25, 17, -16, 12, -11, 3, 29, 29, -29],
 [0, -15, -12, 3, 18, -17, -7, -3, 17, 1],
 [0, 0, 18, 14, 17, -22, -7, 5, 25, -2],
 [0, 0, 0, 17, -8, -4, 0, 12, -24, 18],
 [0, 0, 0, 0, 11, 11, -21, 28, 13, 3],
 [0, 0, 0, 0, 0, -23, 22, -17, -24, -24],
 [0, 0, 0, 0, 0, 0, -9, 15, -5, 27],
 [0, 0, 0, 0, 0, 0, 0, -20, -14, 3],
 [0, 0, 0, 0, 0, 0, 0, 0, 25, -7],
 [0, 0, 0, 0, 0, 0, 0, 0, 0, 18]]? Round to the nearest integer, then express your answer modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:
[[15, 10, 10, -10, 29, 26, 7, -23, 12, 1],
 [0, 13, -21, -8, -27, 17, 21, 7, -1, 10],
 [0, 0, -10, 25, -25, 18, -14, -6, -7, -9],
 [0, 0, 0, 3, -5, -12, -5, 29, -28, -29],
 [0, 0, 0, 0, -27, 18, 7, 8, -11, -25],
 [0, 0, 0, 0, 0, 5, -5, -3, -26, 20],
 [0, 0, 0, 0, 0, 0, -26, 6, 9, -9],
 [0, 0, 0, 0, 0, 0, 0, 14, 27, -3],
 [0, 0, 0, 0, 0, 0, 0, 0, -27, 23],
 [0, 0, 0, 0, 0, 0, 0, 0, 0, -22]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:
[[0, -5, -16, -2, 0, 8, 8, -4, -10, -19],
 [-5, -28, -7, 4, 4, -6, -23, -4, 12, -17],
 [-16, -7, 19, -16, 4, 9, -6, 7, 14, 22],
 [-2, 4, -16, 8, 12, -14, -10, 10, -4, 2],
 [0, 4, 4, 12, 22, 6, -10, -23, -4, 13],
 [8, -6, 9, -14, 6, 1, -4, 14, -9, -26],
 [8, -23, -6, -10, -10, -4, -21, 8, -10, 15],
 [-4, -4, 7, 10, -23, 14, 8, 6, -11, -8],
 [-10, 12, 14, -4, -4, -9, -10, -11, -23, -10],
 [-19, -17, 22, 2, 13, -26, 15, -8, -10, -13]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute |A| for the matrix A =
[[13, 7, -12, 17, 22, 24, 25, 30, 1, 15],
 [0, 5, -13, -21, 1, -13, -19, 20, -23, 2],
 [0, 0, 7, -17, -29, -22, 30, 13, -26, 3],
 [0, 0, 0, 11, -14, -5, 15, -4, 12, -3],
 [0, 0, 0, 0, -12, 1, -12, -7, -7, 25],
 [0, 0, 0, 0, 0, 10, -8, 25, 17, -13],
 [0, 0, 0, 0, 0, 0, 2, -7, 30, 24],
 [0, 0, 0, 0, 0, 0, 0, -23, -21, -30],
 [0, 0, 0, 0, 0, 0, 0, 0, 29, 20],
 [0, 0, 0, 0, 0, 0, 0, 0, 0, -24]]
Round to the nearest integer, then take the result modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the value of det(A) where A =
[[-6, 19, -17, 13, 15, -5, -13, -11, 3, -24],
 [0, 29, -21, -16, -14, -20, 3, -4, -10, 0],
 [0, 0, -27, 10, 28, 29, 18, -14, 18, 17],
 [0, 0, 0, -8, -16, 2, -12, 26, -16, 10],
 [0, 0, 0, 0, 17, 1, -9, 12, 1, -18],
 [0, 0, 0, 0, 0, 30, 18, 2, -4, -26],
 [0, 0, 0, 0, 0, 0, -29, -18, 11, 22],
 [0, 0, 0, 0, 0, 0, 0, 23, 20, -11],
 [0, 0, 0, 0, 0, 0, 0, 0, -27, 21],
 [0, 0, 0, 0, 0, 0, 0, 0, 0, 5]]
Round to the nearest integer, then give your answer as det(A) mod 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the value of det(A) where A =
[[-17, 17, -12, 11, -8, 10, 21, 18, -18, 16],
 [17, 12, -15, 9, 7, -8, -6, 4, 10, 7],
 [-12, -15, 14, 6, -14, 12, 14, 10, 4, -12],
 [11, 9, 6, -6, -2, 0, -14, 22, -8, -10],
 [-8, 7, -14, -2, -16, 2, -1, 4, -11, 1],
 [10, -8, 12, 0, 2, 24, 24, 2, -4, -14],
 [21, -6, 14, -14, -1, 24, -1, -11, 14, 15],
 [18, 4, 10, 22, 4, 2, -11, -25, -23, -3],
 [-18, 10, 4, -8, -11, -4, 14, -23, -28, 12],
 [16, 7, -12, -10, 1, -14, 15, -3, 12, 0]]
Round to the nearest integer, then give your answer as det(A) mod 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:
[[-19, -20, 20, -20, 3, 16, 6, 19, -2, 22],
 [22, 17, 5, -4, 24, 11, -9, -29, 16, 5],
 [30, 17, -1, 28, -24, 26, 26, -19, -28, -14],
 [10, 1, -23, -8, 7, -1, -16, -21, 24, 28],
 [26, 7, -16, -1, 15, -5, 20, 14, -17, -28],
 [5, -5, 30, -17, 0, -17, 27, 9, -21, -22],
 [15, 9, 12, 11, -13, 5, 5, -19, 19, 30],
 [9, -28, -13, -24, 0, -30, 0, 23, -18, -2],
 [-28, -2, 4, -16, -10, -12, -3, -27, 14, -18],
 [-16, 20, 17, 8, 1, -28, -1, 27, -11, -29]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:
[[3, -15, -13, -13, 7, 19, 12, 1, -24, -8],
 [-8, 15, 30, -13, -24, 11, 9, -7, -17, 19],
 [-26, 15, 23, 26, -9, 27, -9, -21, -5, -16],
 [7, 10, 11, 24, 18, -30, -17, 5, 0, -3],
 [3, 4, 29, 8, -8, 15, 13, -12, 30, -13],
 [-16, 30, 30, -30, -6, -5, 4, 26, -16, -27],
 [-16, 11, 7, 14, 8, 27, 23, -30, -9, -20],
 [15, 7, 6, 20, -5, 20, -4, 27, -18, -24],
 [-23, 15, 20, 20, -8, -5, 13, 24, -4, -22],
 [15, 7, 16, -18, -24, -20, -21, 2, 8, 19]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:
[[-8, 6, 22, -21, 1, -18, 6, -2, 16, -22],
 [6, 5, -12, -16, -14, 26, -4, -9, 13, 28],
 [22, -12, -8, 4, 8, 20, 22, -11, 2, 22],
 [-21, -16, 4, 23, 14, 20, 4, 20, -8, -17],
 [1, -14, 8, 14, 8, 8, 15, -6, -15, -20],
 [-18, 26, 20, 20, 8, 6, 3, -11, 0, -4],
 [6, -4, 22, 4, 15, 3, 16, -10, -16, 2],
 [-2, -9, -11, 20, -6, -11, -10, 6, 17, -1],
 [16, 13, 2, -8, -15, 0, -16, 17, 15, -4],
 [-22, 28, 22, -17, -20, -4, 2, -1, -4, -10]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:
[[14, 0, 6, 27, 25, -12, -8, 4, 23, 19],
 [-25, -25, 25, 6, -1, -30, -23, -3, -6, 2],
 [22, 29, 7, 21, -17, -20, -29, 22, -1, -1],
 [-27, -18, -24, 7, -28, -22, -17, 21, -20, 6],
 [-17, -12, -23, 28, -24, 28, 28, -24, 25, 24],
 [-28, -28, -13, 14, 2, 6, -3, 5, -15, -16],
 [-2, 28, -13, 18, 15, 15, -12, -2, -25, 14],
 [19, 27, 16, 30, 24, -4, -24, -4, -12, -14],
 [10, -20, -26, -29, 16, 25, -19, 11, 11, 21],
 [-20, -21, -3, -24, -17, -18, -26, 30, 20, 11]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute |A| for the matrix A =
[[5, -24, -20, 4, -4, -18, -10, -2, 10, -19],
 [-24, 25, 2, 11, -2, -20, -2, 12, 2, 26],
 [-20, 2, 11, 20, -10, 20, 0, -16, 5, -13],
 [4, 11, 20, -11, -10, 23, 4, 18, 15, -4],
 [-4, -2, -10, -10, -9, -22, 16, 5, -18, -7],
 [-18, -20, 20, 23, -22, 4, 18, 4, 2, 4],
 [-10, -2, 0, 4, 16, 18, 16, -8, 5, -20],
 [-2, 12, -16, 18, 5, 4, -8, -19, 14, -16],
 [10, 2, 5, 15, -18, 2, 5, 14, 15, -6],
 [-19, 26, -13, -4, -7, 4, -20, -16, -6, 13]]
Round to the nearest integer, then take the result modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute |A| for the matrix A =
[[18, -6, 5, -14, 0, -5, -15, -2, 10, 18],
 [-6, -6, -12, 16, -25, -9, -2, 12, -14, -14],
 [5, -12, 27, -1, 6, 20, -20, 6, -10, 14],
 [-14, 16, -1, -27, -26, 12, -2, 0, -17, 2],
 [0, -25, 6, -26, 3, 16, -15, -23, 4, 8],
 [-5, -9, 20, 12, 16, 5, 18, -14, -30, 10],
 [-15, -2, -20, -2, -15, 18, 7, 6, -10, 16],
 [-2, 12, 6, 0, -23, -14, 6, 14, 10, -10],
 [10, -14, -10, -17, 4, -30, -10, 10, -9, 12],
 [18, -14, 14, 2, 8, 10, 16, -10, 12, 4]]
Round to the nearest integer, then take the result modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute |A| for the matrix A =
[[-21, 25, 16, -28, -29, 23, 6, 25, 0, 2],
 [1, 12, -19, 27, -28, 24, 30, 17, -5, -17],
 [-19, 21, -5, -15, 22, -23, 18, 18, -3, -24],
 [-16, 30, 29, 10, 5, -23, -21, -16, 24, -13],
 [15, 6, 10, 14, 30, 26, 20, 12, 13, 4],
 [-29, 24, -9, -16, 6, 8, 5, -26, 26, 17],
 [-16, -4, -15, 26, 5, 7, -13, 4, -6, -9],
 [25, 0, 28, 6, 3, -8, -15, -25, 28, -16],
 [-13, 7, -18, -7, -18, -30, 17, 5, 18, -13],
 [17, 2, 7, 12, -25, -14, -27, -17, -1, 15]]
Round to the nearest integer, then take the result modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:
[[-8, -10, 8, 0, 26, -26, 24, -12, -16, 13],
 [-10, -29, -4, -4, 8, -8, 24, -2, -1, -21],
 [8, -4, -24, 8, -2, 1, -2, -6, -15, -14],
 [0, -4, 8, -15, -2, -27, -10, -13, -12, 2],
 [26, 8, -2, -2, 11, 26, 2, 8, 14, 3],
 [-26, -8, 1, -27, 26, 15, 2, 29, -11, -4],
 [24, 24, -2, -10, 2, 2, -20, -24, 18, 14],
 [-12, -2, -6, -13, 8, 29, -24, -23, -9, 24],
 [-16, -1, -15, -12, 14, -11, 18, -9, 27, 0],
 [13, -21, -14, 2, 3, -4, 14, 24, 0, -17]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute |A| for the matrix A =
[[4, -16, 19, 13, -1, 14, 2, 5, 9, 20],
 [0, -1, -5, -10, 6, 12, 26, 0, 25, 25],
 [0, 0, -14, -14, 3, -7, 27, 2, -27, -22],
 [0, 0, 0, 7, 14, -16, 12, 11, -28, 0],
 [0, 0, 0, 0, 22, 24, 26, 25, 28, -8],
 [0, 0, 0, 0, 0, 1, -14, 23, 6, -7],
 [0, 0, 0, 0, 0, 0, -21, -5, 16, -25],
 [0, 0, 0, 0, 0, 0, 0, -19, 27, -10],
 [0, 0, 0, 0, 0, 0, 0, 0, 24, -12],
 [0, 0, 0, 0, 0, 0, 0, 0, 0, -22]]
Round to the nearest integer, then take the result modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:
[[-2, -28, 2, -1, 5, -22, -30, 17, -8, -28],
 [0, -7, -25, -18, 18, -16, 27, 22, -1, -19],
 [0, 0, 28, 17, 4, -3, 29, -27, -24, 16],
 [0, 0, 0, 15, 24, 14, 10, -6, 19, -28],
 [0, 0, 0, 0, -9, -4, 25, -29, -9, 26],
 [0, 0, 0, 0, 0, -11, -7, 14, 0, 21],
 [0, 0, 0, 0, 0, 0, 26, 28, -27, 4],
 [0, 0, 0, 0, 0, 0, 0, 16, -26, 30],
 [0, 0, 0, 0, 0, 0, 0, 0, -9, 1],
 [0, 0, 0, 0, 0, 0, 0, 0, 0, -20]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:
[[11, -30, 18, 6, 18, 4, 10, -28, 4, -2],
 [0, 6, 29, 25, 11, 16, -6, -19, 7, -24],
 [0, 0, -27, 30, 14, 16, 0, 19, 19, 8],
 [0, 0, 0, -5, -8, -2, -23, -12, -2, 12],
 [0, 0, 0, 0, 25, -21, 20, 29, -17, 21],
 [0, 0, 0, 0, 0, 6, 17, 27, 8, -3],
 [0, 0, 0, 0, 0, 0, 1, 21, -26, -28],
 [0, 0, 0, 0, 0, 0, 0, -2, 17, 7],
 [0, 0, 0, 0, 0, 0, 0, 0, -5, -14],
 [0, 0, 0, 0, 0, 0, 0, 0, 0, -14]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:
[[11, 19, -29, 14, 1, 16, -3, 25, -27, -24],
 [0, -6, 17, 27, -22, -8, -8, 18, -5, 9],
 [0, 0, -4, 14, -29, -30, 17, -15, 12, -7],
 [0, 0, 0, -25, -5, -2, 12, 27, -30, -22],
 [0, 0, 0, 0, -28, 30, -22, -29, 29, -21],
 [0, 0, 0, 0, 0, -25, 7, 10, 11, 16],
 [0, 0, 0, 0, 0, 0, 10, 12, 0, 22],
 [0, 0, 0, 0, 0, 0, 0, -24, -26, -29],
 [0, 0, 0, 0, 0, 0, 0, 0, -22, -8],
 [0, 0, 0, 0, 0, 0, 0, 0, 0, 7]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the determinant of the matrix:
[[5, -28, 12, -2, 2, -17, 7, -2, -8, 28],
 [-14, 28, 18, 24, -20, -3, 23, -24, 14, 9],
 [-23, 10, -2, -6, -24, 26, -9, -22, -20, 3],
 [-4, 19, -9, -28, 19, 17, 9, 24, -23, -25],
 [26, -6, -29, -15, 27, 22, 10, 20, -10, -16],
 [25, 3, 16, 23, 12, -11, 13, 0, -16, 17],
 [-3, -25, -28, 7, -8, 27, -28, 22, 14, 13],
 [-23, -29, -24, 30, -14, -24, 2, 5, 16, -27],
 [13, -15, -10, -13, 15, 15, -3, 12, 29, -15],
 [16, -9, -25, -1, 25, 14, 27, -3, -14, 5]]? Round to the nearest integer, then express your answer modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute |A| for the matrix A =
[[17, -6, 21, -20, -25, 23, 9, 4, -4, -6],
 [-6, -16, 3, 8, -14, 22, 2, 17, 22, 8],
 [21, 3, 27, -10, 6, 6, 10, 8, -8, -18],
 [-20, 8, -10, -26, 10, 14, 16, 14, 15, -6],
 [-25, -14, 6, 10, -11, -8, -10, 9, -22, 15],
 [23, 22, 6, 14, -8, 19, -1, -26, -11, -8],
 [9, 2, 10, 16, -10, -1, -19, -10, -26, 8],
 [4, 17, 8, 14, 9, -26, -10, 3, 14, 8],
 [-4, 22, -8, 15, -22, -11, -26, 14, 6, 25],
 [-6, 8, -18, -6, 15, -8, 8, 8, 25, -4]]
Round to the nearest integer, then take the result modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the value of det(A) where A =
[[-26, -12, -23, 6, 0, -4, -18, 11, -25, -30],
 [0, -20, 21, 10, 0, -15, -16, -26, -16, -30],
 [0, 0, 29, 17, 23, 8, 24, -23, 22, -9],
 [0, 0, 0, -1, -19, 27, 29, -29, 15, 20],
 [0, 0, 0, 0, -14, 4, 21, 26, 11, 25],
 [0, 0, 0, 0, 0, 26, 19, -12, -14, -23],
 [0, 0, 0, 0, 0, 0, -12, -3, 25, -3],
 [0, 0, 0, 0, 0, 0, 0, 10, 7, -19],
 [0, 0, 0, 0, 0, 0, 0, 0, 30, -1],
 [0, 0, 0, 0, 0, 0, 0, 0, 0, 5]]
Round to the nearest integer, then give your answer as det(A) mod 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute |A| for the matrix A =
[[21, -28, 3, -19, 25, 27, 14, -4, 19, 6],
 [24, -6, -19, 20, 2, -22, -30, 25, 19, -8],
 [-3, -28, 7, 23, 5, 25, 13, 13, -26, 24],
 [-2, 22, -18, 13, -27, -25, 20, 7, -25, -20],
 [-4, 23, 15, 28, 4, 30, 9, -27, -4, -15],
 [-13, -24, -20, -23, 28, 21, -25, 25, 17, -26],
 [26, -25, 7, 29, 30, -29, 0, 8, 1, -22],
 [-16, -10, 15, 22, -3, 14, -4, -26, -14, 6],
 [27, -7, 0, 4, 10, 10, 23, -27, -11, 12],
 [-14, 15, -21, 6, -10, -10, 29, 18, -15, 2]]
Round to the nearest integer, then take the result modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:
[[17, -23, 25, 1, -5, 23, -13, 6, 21, -19],
 [7, 3, -27, -15, 30, -7, -17, -14, 20, 0],
 [-27, 19, 13, 3, 7, 7, -28, -23, -19, 4],
 [-29, 22, -2, -8, 2, 19, -13, 9, 27, -9],
 [-17, -2, 14, -16, -16, 14, -27, 5, -26, -28],
 [-19, -11, 13, -11, 8, 8, -30, 13, -28, 16],
 [-22, 23, 23, -11, 27, -22, 0, 15, -3, 4],
 [9, 30, 7, 13, -29, -28, -17, -14, 4, -27],
 [16, -1, 23, 27, 8, 20, -17, 17, -4, -18],
 [24, 30, -11, 18, 18, -7, -21, -24, 21, -14]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute |A| for the matrix A =
[[11, 1, 1, -12, -2, 2, -29, 27, -20, 16],
 [24, 2, 10, 9, -30, 11, -14, 19, -15, -29],
 [23, 18, -27, 1, -24, -2, 30, 29, -22, 27],
 [4, 21, 22, -26, 19, 30, -10, 27, -14, 8],
 [-17, 1, -16, -10, 23, -17, 10, -15, 20, -30],
 [9, -13, 3, -5, 30, 5, -10, -30, -4, 20],
 [-20, 25, 7, 20, -17, -3, 24, -4, -9, -10],
 [25, -7, -12, -7, -5, -6, 14, 13, -2, -21],
 [20, -20, -7, -7, -19, -24, 9, -14, 4, -25],
 [-19, -16, 1, -8, -24, 28, 7, 0, -2, 13]]
Round to the nearest integer, then take the result modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute |A| for the matrix A =
[[24, 14, 26, 4, -12, 4, -2, -7, 8, -24],
 [14, 18, 12, -24, -15, -15, 7, 15, 4, 9],
 [26, 12, 24, 2, -18, 3, 18, 11, 16, 5],
 [4, -24, 2, -15, 20, -12, 6, -16, 0, 23],
 [-12, -15, -18, 20, -4, -26, 11, -17, -18, 8],
 [4, -15, 3, -12, -26, -12, 20, -10, -2, -3],
 [-2, 7, 18, 6, 11, 20, 12, -3, -22, 10],
 [-7, 15, 11, -16, -17, -10, -3, 10, 18, 5],
 [8, 4, 16, 0, -18, -2, -22, 18, -20, 7],
 [-24, 9, 5, 23, 8, -3, 10, 5, 7, -7]]
Round to the nearest integer, then take the result modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:
[[-3, -1, 9, -14, 26, 25, -13, -6, -27, -5],
 [0, -19, 23, 17, -13, -21, 5, -29, 29, -6],
 [16, -22, 16, 1, -26, 20, -28, -14, -18, 25],
 [-28, -3, -27, -13, 25, 4, -17, -15, -19, -20],
 [-29, 2, -18, -1, -5, 19, -13, -18, -27, 28],
 [2, -16, -14, -25, -26, 2, 23, -15, 15, -7],
 [30, -26, -28, 4, 30, -4, -19, 19, 10, -6],
 [24, -14, 18, -11, -3, 19, 30, 4, 19, -16],
 [2, -28, -24, -21, 10, -5, 10, 9, -25, 2],
 [-15, -7, 25, -1, 29, 26, -21, -20, 13, -9]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute |A| for the matrix A =
[[8, -12, 24, 19, -30, -20, 10, 11, -21, -30],
 [0, -14, 28, 13, 13, 20, -14, 8, 24, 12],
 [0, 0, 17, -8, 10, 28, -21, 22, 11, -1],
 [0, 0, 0, 29, 15, -12, -13, -13, 15, 4],
 [0, 0, 0, 0, 13, -22, 1, -5, -2, 28],
 [0, 0, 0, 0, 0, 26, 4, -19, -23, -6],
 [0, 0, 0, 0, 0, 0, -18, -20, 7, -25],
 [0, 0, 0, 0, 0, 0, 0, -6, -22, -11],
 [0, 0, 0, 0, 0, 0, 0, 0, -9, 25],
 [0, 0, 0, 0, 0, 0, 0, 0, 0, -26]]
Round to the nearest integer, then take the result modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the determinant of the matrix:
[[25, -29, -19, 28, 26, 29, 24, -24, -29, -23],
 [-22, 27, -4, -3, 6, -16, -12, -1, 20, -18],
 [14, -25, -1, -30, 11, 28, 26, 7, -6, 4],
 [-5, -18, -12, -21, 14, -24, -16, -8, 5, 12],
 [0, -23, 28, -1, 3, 2, -30, -15, 19, -20],
 [-4, -9, 9, -12, 13, -25, 25, 26, 17, 9],
 [8, -11, -28, 24, -30, -8, 7, -28, 20, 3],
 [-14, 17, -4, 22, 30, 8, -8, 7, -20, -16],
 [-5, 23, -20, -24, 16, 17, -23, -26, -14, -8],
 [-29, -4, -10, -24, 24, 26, 22, 7, -5, -1]]? Round to the nearest integer, then express your answer modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the determinant of the matrix:
[[6, 26, -22, 4, 8, 14, -5, -4, -10, 14],
 [26, -8, -4, -4, -8, -14, -12, 19, -4, -2],
 [-22, -4, -5, 2, -13, -4, 4, -10, 2, -20],
 [4, -4, 2, -18, -19, -27, -16, 20, 6, 10],
 [8, -8, -13, -19, 11, 4, 2, 20, 18, 15],
 [14, -14, -4, -27, 4, 22, -8, 2, 4, -16],
 [-5, -12, 4, -16, 2, -8, 29, 10, 2, 10],
 [-4, 19, -10, 20, 20, 2, 10, -21, 22, -3],
 [-10, -4, 2, 6, 18, 4, 2, 22, -8, 14],
 [14, -2, -20, 10, 15, -16, 10, -3, 14, 19]]? Round to the nearest integer, then express your answer modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute |A| for the matrix A =
[[-6, -3, -19, -8, -14, 27, 27, 10, 6, -13],
 [24, -22, 14, 4, 5, 26, -13, -11, -10, 16],
 [-11, 24, -25, -22, 12, -2, -2, -18, 5, -4],
 [16, 26, 18, 13, -25, 8, 26, 1, 18, 12],
 [13, -3, 14, -30, 19, 23, 20, 12, 0, -1],
 [23, -13, -2, 11, 7, -8, -9, -29, -26, 11],
 [-16, 30, 1, 15, -25, -17, -7, 26, -10, -17],
 [-19, 24, -27, 27, 13, -10, -14, -2, 20, -15],
 [-13, 7, 10, 27, 20, 13, -20, 1, -3, -15],
 [3, 19, -1, 7, 27, -9, -26, -22, -18, 8]]
Round to the nearest integer, then take the result modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:
[[26, 24, -22, 5, -24, -3, -21, -15, -21, 8],
 [27, -5, 3, 3, 9, -17, -13, -30, -14, 18],
 [-9, 6, -15, -24, -16, 20, -10, -29, 28, 17],
 [-6, -22, -11, 19, -21, 25, 21, -10, -27, -1],
 [3, -1, -17, -9, -30, 29, -23, -20, -30, -26],
 [26, 14, 18, -21, 24, 8, -18, -10, 5, 26],
 [22, 14, 2, 26, 12, -3, 22, -22, 14, -20],
 [28, 9, -2, 29, 27, -24, 30, -4, 29, -9],
 [26, 0, -1, -3, -11, -16, -16, 22, -19, -14],
 [-8, -25, 14, -15, -4, -8, -30, 14, -24, 14]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the value of det(A) where A =
[[14, 12, 20, 7, -23, 20, 6, 11, 2, -5],
 [0, 27, 25, 8, -23, -13, 8, -17, 21, -13],
 [0, 0, -8, -27, -21, 12, -20, -11, -12, -30],
 [0, 0, 0, 18, -26, 3, -27, -4, 8, 22],
 [0, 0, 0, 0, -30, 27, 21, 22, -15, 27],
 [0, 0, 0, 0, 0, -9, 30, 13, -11, 25],
 [0, 0, 0, 0, 0, 0, -18, 17, -17, 10],
 [0, 0, 0, 0, 0, 0, 0, 4, 30, 5],
 [0, 0, 0, 0, 0, 0, 0, 0, -13, -23],
 [0, 0, 0, 0, 0, 0, 0, 0, 0, 9]]
Round to the nearest integer, then give your answer as det(A) mod 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute |A| for the matrix A =
[[20, 14, -19, 26, -4, -5, 17, -2, -8, 18],
 [0, -11, 7, 15, -15, 0, -28, -10, 20, 8],
 [0, 0, 27, 24, -8, 1, 11, -22, -28, -4],
 [0, 0, 0, -7, -8, -22, -29, -25, 6, 4],
 [0, 0, 0, 0, 5, -8, -2, -18, 24, -26],
 [0, 0, 0, 0, 0, 25, 12, -30, -11, 12],
 [0, 0, 0, 0, 0, 0, 4, 21, 3, 19],
 [0, 0, 0, 0, 0, 0, 0, -22, 16, 27],
 [0, 0, 0, 0, 0, 0, 0, 0, 11, -3],
 [0, 0, 0, 0, 0, 0, 0, 0, 0, -14]]
Round to the nearest integer, then take the result modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the value of det(A) where A =
[[-7, 25, 2, -23, 28, -3, -12, -20, 24, -21],
 [0, -30, -26, -15, -11, -11, -3, -26, 17, -28],
 [0, 0, 3, 18, 23, -3, -30, 17, -4, 24],
 [0, 0, 0, 1, 21, -24, 12, 7, 3, 15],
 [0, 0, 0, 0, -2, 29, 3, 3, 14, 14],
 [0, 0, 0, 0, 0, 29, -14, -2, 2, 8],
 [0, 0, 0, 0, 0, 0, -13, -30, -20, 23],
 [0, 0, 0, 0, 0, 0, 0, 18, -19, -1],
 [0, 0, 0, 0, 0, 0, 0, 0, 30, 21],
 [0, 0, 0, 0, 0, 0, 0, 0, 0, -22]]
Round to the nearest integer, then give your answer as det(A) mod 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the value of det(A) where A =
[[19, 21, -6, -13, -4, -8, -5, 12, 0, 4],
 [21, -2, 10, 17, -6, 2, 12, -7, -26, -6],
 [-6, 10, 19, 2, -6, 12, 13, -4, 1, -1],
 [-13, 17, 2, -16, 7, -14, -2, -26, -8, 16],
 [-4, -6, -6, 7, 24, -10, 20, -6, 12, 8],
 [-8, 2, 12, -14, -10, 26, 15, 13, 8, -2],
 [-5, 12, 13, -2, 20, 15, -19, -3, -3, -21],
 [12, -7, -4, -26, -6, 13, -3, -24, -9, 11],
 [0, -26, 1, -8, 12, 8, -3, -9, -4, 2],
 [4, -6, -1, 16, 8, -2, -21, 11, 2, -30]]
Round to the nearest integer, then give your answer as det(A) mod 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute |A| for the matrix A =
[[-16, -24, 18, 7, 18, 22, 14, 21, 2, -2],
 [-24, -12, 7, 10, 9, 2, 0, -13, 9, -19],
 [18, 7, -15, -20, -4, 15, 0, 28, 4, -4],
 [7, 10, -20, 20, 28, -21, -6, 18, -8, 10],
 [18, 9, -4, 28, -10, -12, -12, -28, 6, -20],
 [22, 2, 15, -21, -12, 0, 17, 2, 12, -14],
 [14, 0, 0, -6, -12, 17, 5, 2, 8, 18],
 [21, -13, 28, 18, -28, 2, 2, -18, 2, 16],
 [2, 9, 4, -8, 6, 12, 8, 2, 16, 0],
 [-2, -19, -4, 10, -20, -14, 18, 16, 0, -3]]
Round to the nearest integer, then take the result modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:
[[-27, 18, 7, -2, 18, -5, -6, -17, 6, 19],
 [-3, -23, 11, -20, 23, 30, 4, 28, 0, 3],
 [27, 28, 15, 5, -14, 18, -10, -5, 10, -3],
 [22, -9, 27, 10, -28, -3, 5, -29, 15, -11],
 [9, 19, 5, -23, 8, -6, -16, -1, 16, 3],
 [-27, 26, -9, -6, -22, -8, 8, 25, 19, 27],
 [-19, -17, -24, 0, -25, -8, 23, 28, -12, -10],
 [-12, 23, 16, -12, 13, 3, 12, -18, 5, -6],
 [2, 25, -10, 3, 15, -6, -13, 12, -20, -12],
 [18, 18, 3, -29, -1, 14, 7, -16, -20, -7]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the determinant of the matrix:
[[14, 30, -29, -5, -13, -29, 9, -28, -14, -7],
 [0, -25, 9, -5, 26, 18, 26, 25, -25, -19],
 [0, 0, -25, 3, 28, -28, 10, -12, -2, 1],
 [0, 0, 0, -2, -18, -11, -3, -4, -18, -6],
 [0, 0, 0, 0, -16, 14, 14, -1, 27, 7],
 [0, 0, 0, 0, 0, 2, -19, -8, -26, 12],
 [0, 0, 0, 0, 0, 0, 19, -30, -9, -3],
 [0, 0, 0, 0, 0, 0, 0, 21, 7, 14],
 [0, 0, 0, 0, 0, 0, 0, 0, -18, -27],
 [0, 0, 0, 0, 0, 0, 0, 0, 0, -15]]? Round to the nearest integer, then express your answer modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:
[[7, 22, 11, -23, -20, -11, -7, 28, 20, -24],
 [29, -10, 13, 22, -25, 0, -19, 6, -18, 18],
 [0, -22, -4, 21, 22, -14, 20, 20, -23, -4],
 [9, 26, 27, -16, 8, -25, 1, 17, -23, 4],
 [0, 11, -5, 11, -7, 20, 30, -29, 10, -30],
 [-21, 27, 19, -8, 2, 13, 6, 29, 26, 26],
 [-20, -11, -5, 15, 16, -29, -6, 28, -27, -12],
 [-18, -12, -18, 24, -19, -29, 6, 19, -8, 24],
 [-12, -28, -7, -8, -27, -13, -19, 30, 4, -4],
 [12, -17, 28, 0, -28, -26, -2, 8, 21, -14]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:
[[16, -10, -29, -8, -15, -20, 23, 28, -22, -29],
 [-13, -18, 14, -23, -21, -4, -14, -7, -10, -30],
 [-15, 27, 12, 2, -25, -19, 1, 17, 27, -20],
 [-13, -29, 1, 18, 18, -11, -10, 5, 7, 25],
 [-4, 16, -20, -13, -14, 3, 14, -5, 28, -25],
 [12, -1, 21, 8, 19, 1, -14, -18, 22, 15],
 [10, -18, -25, -9, 2, 2, -27, -17, 19, 17],
 [4, -4, -25, 27, 30, -30, 12, -3, -2, 1],
 [-3, -4, -21, -13, -27, 7, 30, 20, 10, 11],
 [21, 24, 1, 28, -26, -9, 26, 17, 26, -9]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:
[[22, -27, 5, 30, -10, -9, -21, -8, -26, 30],
 [0, 29, -19, 26, -1, 26, 2, 6, -13, -27],
 [0, 0, -8, 27, -25, -24, -12, 15, -16, 22],
 [0, 0, 0, -16, 28, -25, -25, 26, -25, -19],
 [0, 0, 0, 0, -25, 26, 11, 30, 20, 25],
 [0, 0, 0, 0, 0, 20, -24, 23, -13, 27],
 [0, 0, 0, 0, 0, 0, 4, 16, -21, 22],
 [0, 0, 0, 0, 0, 0, 0, 28, -28, 8],
 [0, 0, 0, 0, 0, 0, 0, 0, -11, -4],
 [0, 0, 0, 0, 0, 0, 0, 0, 0, -11]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the determinant of the matrix:
[[4, 11, -4, 14, -1, 8, 15, 27, -1, 28],
 [0, 25, -10, -5, -7, 23, -9, 6, 12, -5],
 [0, 0, 2, -7, -26, -7, 4, 27, -9, 2],
 [0, 0, 0, -1, -5, -18, -25, -28, 30, -20],
 [0, 0, 0, 0, -21, -20, -15, -11, 11, 13],
 [0, 0, 0, 0, 0, -8, -10, 8, -26, 20],
 [0, 0, 0, 0, 0, 0, 21, -16, 18, -12],
 [0, 0, 0, 0, 0, 0, 0, 25, 20, -11],
 [0, 0, 0, 0, 0, 0, 0, 0, -29, 21],
 [0, 0, 0, 0, 0, 0, 0, 0, 0, -5]]? Round to the nearest integer, then express your answer modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:
[[-6, -29, -9, 6, 13, -16, -25, 27, 2, -20],
 [0, -19, -7, -28, -1, -12, 14, 30, 12, 24],
 [0, 0, 19, -2, 17, -23, -10, 26, -18, 18],
 [0, 0, 0, -7, 10, -22, -21, -20, 2, 18],
 [0, 0, 0, 0, 7, -1, 24, -23, -4, -9],
 [0, 0, 0, 0, 0, 27, 24, -20, -24, 24],
 [0, 0, 0, 0, 0, 0, -30, -2, -7, 24],
 [0, 0, 0, 0, 0, 0, 0, 10, -19, -23],
 [0, 0, 0, 0, 0, 0, 0, 0, -26, -30],
 [0, 0, 0, 0, 0, 0, 0, 0, 0, -17]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the determinant of the matrix:
[[-12, -2, -20, 14, 6, -3, 8, 18, -25, -19],
 [-2, -13, -10, 14, 20, -9, -2, 3, 6, 18],
 [-20, -10, 29, -10, -15, -14, -8, -2, -18, 8],
 [14, 14, -10, -4, 26, -24, -6, 12, 6, 21],
 [6, 20, -15, 26, 22, 2, 15, 5, 1, 1],
 [-3, -9, -14, -24, 2, -1, 18, -5, -12, 22],
 [8, -2, -8, -6, 15, 18, 15, 25, -5, -7],
 [18, 3, -2, 12, 5, -5, 25, -14, -2, -2],
 [-25, 6, -18, 6, 1, -12, -5, -2, -5, -14],
 [-19, 18, 8, 21, 1, 22, -7, -2, -14, -11]]? Round to the nearest integer, then express your answer modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the determinant of the matrix:
[[14, -22, -10, 13, 1, 13, -21, -2, 3, 26],
 [0, -26, -20, 27, -3, -7, 3, 22, 11, 9],
 [0, 0, -5, 12, 10, -24, 13, -24, 17, 26],
 [0, 0, 0, 15, 14, 30, -28, 14, 30, -5],
 [0, 0, 0, 0, 16, -28, 7, -2, -6, 15],
 [0, 0, 0, 0, 0, -13, 21, 7, 5, -19],
 [0, 0, 0, 0, 0, 0, -29, 27, 3, 27],
 [0, 0, 0, 0, 0, 0, 0, -10, 30, 7],
 [0, 0, 0, 0, 0, 0, 0, 0, -11, -8],
 [0, 0, 0, 0, 0, 0, 0, 0, 0, 30]]? Round to the nearest integer, then express your answer modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute |A| for the matrix A =
[[16, -27, 2, 2, -25, 23, 10, -17, 15, 28],
 [0, -25, 20, -28, 6, -9, 7, -23, -7, -18],
 [0, 0, 20, 22, 10, 5, 1, -26, 18, -24],
 [0, 0, 0, -3, 2, 15, -17, -18, -2, 19],
 [0, 0, 0, 0, 18, -4, -1, 3, 15, -30],
 [0, 0, 0, 0, 0, -13, 4, 19, -12, -18],
 [0, 0, 0, 0, 0, 0, -23, -8, -23, 26],
 [0, 0, 0, 0, 0, 0, 0, 11, 11, 19],
 [0, 0, 0, 0, 0, 0, 0, 0, -24, -2],
 [0, 0, 0, 0, 0, 0, 0, 0, 0, -30]]
Round to the nearest integer, then take the result modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:
[[-28, -13, -10, -2, 21, 22, 11, 21, 5, 0],
 [0, 1, -15, -9, -29, 20, -16, 9, -14, -18],
 [0, 0, -6, -21, 14, -20, 2, -17, 3, -9],
 [0, 0, 0, -5, -30, -21, 5, -29, -2, -6],
 [0, 0, 0, 0, 29, -6, -18, 9, 3, 4],
 [0, 0, 0, 0, 0, -9, -6, 24, -17, -12],
 [0, 0, 0, 0, 0, 0, -1, -26, -1, -24],
 [0, 0, 0, 0, 0, 0, 0, -6, -18, 17],
 [0, 0, 0, 0, 0, 0, 0, 0, -1, -8],
 [0, 0, 0, 0, 0, 0, 0, 0, 0, 14]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:
[[8, 3, -21, 2, 20, 24, -12, -29, 16, 18],
 [0, -1, 8, -12, -10, 28, 23, 13, -17, 0],
 [0, 0, 22, 20, -7, 6, 9, 10, 3, 16],
 [0, 0, 0, 18, 11, -19, 10, 27, 29, -7],
 [0, 0, 0, 0, 7, -10, 22, -28, 18, -17],
 [0, 0, 0, 0, 0, 11, 13, 26, -1, 14],
 [0, 0, 0, 0, 0, 0, -12, -1, -11, 21],
 [0, 0, 0, 0, 0, 0, 0, -17, -25, 2],
 [0, 0, 0, 0, 0, 0, 0, 0, 25, -20],
 [0, 0, 0, 0, 0, 0, 0, 0, 0, -3]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the value of det(A) where A =
[[-15, -20, -26, 7, -28, 28, -29, 22, 7, -21],
 [0, -10, 0, 3, 18, 1, -2, 27, 23, -30],
 [0, 0, -14, 3, 18, -15, -24, 5, -18, -11],
 [0, 0, 0, 29, -22, 12, -19, -17, -16, -26],
 [0, 0, 0, 0, -6, -27, 20, -5, -20, -25],
 [0, 0, 0, 0, 0, -9, 4, 25, 0, -28],
 [0, 0, 0, 0, 0, 0, 21, 6, -1, 1],
 [0, 0, 0, 0, 0, 0, 0, -18, 4, 9],
 [0, 0, 0, 0, 0, 0, 0, 0, -7, 5],
 [0, 0, 0, 0, 0, 0, 0, 0, 0, -18]]
Round to the nearest integer, then give your answer as det(A) mod 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute |A| for the matrix A =
[[4, 10, 22, 16, -22, -20, -8, 5, -18, -6],
 [10, 9, -6, -7, 6, -16, -27, -26, -18, 18],
 [22, -6, -17, -22, -18, 16, -1, -22, 7, 11],
 [16, -7, -22, 24, 18, -20, 24, -4, 19, -20],
 [-22, 6, -18, 18, 30, -14, 12, -8, 4, 10],
 [-20, -16, 16, -20, -14, 7, -8, 0, -12, 4],
 [-8, -27, -1, 24, 12, -8, -18, -25, -6, -20],
 [5, -26, -22, -4, -8, 0, -25, 17, 13, 14],
 [-18, -18, 7, 19, 4, -12, -6, 13, 18, -16],
 [-6, 18, 11, -20, 10, 4, -20, 14, -16, -29]]
Round to the nearest integer, then take the result modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute |A| for the matrix A =
[[-24, 8, -2, 2, 26, 18, 25, -4, -15, -14],
 [-20, -17, -18, 4, -5, 21, -6, 9, 13, 30],
 [12, 28, -19, 16, 22, -27, 11, 17, 10, 18],
 [-4, 23, 14, -23, 24, -23, -2, -28, -10, 0],
 [-18, 0, -14, 17, 1, -7, -29, 11, -28, -5],
 [-29, 2, 3, -5, 3, 7, -17, 0, -11, -21],
 [-11, 2, 27, 14, 17, 29, -29, 15, 30, 20],
 [-19, -15, -22, -20, -10, -19, -27, -5, -12, 11],
 [16, -14, 28, 13, 30, -30, 17, 27, -23, 27],
 [-1, 26, 20, 10, -7, 12, -14, 23, -1, 10]]
Round to the nearest integer, then take the result modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:
[[12, 2, 11, 2, -14, -15, -26, 4, 10, 14],
 [2, -25, 28, 0, -6, -4, -6, 28, 4, -6],
 [11, 28, -27, 5, 8, 22, 16, -12, -2, 12],
 [2, 0, 5, 5, 2, 26, -1, 0, -7, -19],
 [-14, -6, 8, 2, 28, -10, -4, 7, 26, 28],
 [-15, -4, 22, 26, -10, 12, 1, -2, 9, -5],
 [-26, -6, 16, -1, -4, 1, -13, -7, -6, 16],
 [4, 28, -12, 0, 7, -2, -7, -4, -5, 21],
 [10, 4, -2, -7, 26, 9, -6, -5, -8, -6],
 [14, -6, 12, -19, 28, -5, 16, 21, -6, -2]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:
[[-7, 25, 6, -6, 7, -21, -23, -9, 2, -22],
 [25, 3, 20, -18, -2, -18, 14, 17, 19, -19],
 [6, 20, -2, -2, -9, 14, 1, 9, -20, 10],
 [-6, -18, -2, -26, -2, 0, 2, 20, 0, -4],
 [7, -2, -9, -2, 23, 14, 6, -12, -16, -16],
 [-21, -18, 14, 0, 14, -13, -14, 12, 7, -6],
 [-23, 14, 1, 2, 6, -14, -11, -20, 24, -9],
 [-9, 17, 9, 20, -12, 12, -20, 16, -10, 1],
 [2, 19, -20, 0, -16, 7, 24, -10, -17, 12],
 [-22, -19, 10, -4, -16, -6, -9, 1, 12, 1]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute |A| for the matrix A =
[[15, 24, 5, -1, -20, -1, 28, -9, 22, -29],
 [0, -6, 14, -23, 1, 13, -24, 28, -9, -2],
 [0, 0, 7, 12, 18, -16, 23, 24, -11, -5],
 [0, 0, 0, 18, 21, 11, -27, -27, 17, -30],
 [0, 0, 0, 0, -24, 3, 30, -27, -29, -8],
 [0, 0, 0, 0, 0, 11, 4, 10, -4, -7],
 [0, 0, 0, 0, 0, 0, 5, -26, -15, -13],
 [0, 0, 0, 0, 0, 0, 0, -10, 14, -9],
 [0, 0, 0, 0, 0, 0, 0, 0, -7, -19],
 [0, 0, 0, 0, 0, 0, 0, 0, 0, -18]]
Round to the nearest integer, then take the result modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:
[[30, -13, -6, 7, -29, -10, -8, 2, -4, 30],
 [0, 12, -2, 16, 7, -14, -23, 30, -10, -8],
 [0, 0, -13, 13, -23, 21, -7, -22, -2, -20],
 [0, 0, 0, -27, 15, -7, 18, -29, -19, -19],
 [0, 0, 0, 0, -7, 11, 29, 28, -6, 10],
 [0, 0, 0, 0, 0, 30, 26, -7, 9, 20],
 [0, 0, 0, 0, 0, 0, 21, -13, 1, 22],
 [0, 0, 0, 0, 0, 0, 0, 6, 21, -5],
 [0, 0, 0, 0, 0, 0, 0, 0, -16, 17],
 [0, 0, 0, 0, 0, 0, 0, 0, 0, 22]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:
[[13, 1, -7, -29, 0, -24, 20, -10, 7, -19],
 [0, 17, -15, -9, -20, 8, -17, 11, -18, -15],
 [0, 0, -13, -16, -13, 16, -20, -20, 20, 8],
 [0, 0, 0, 29, -25, 15, -26, 2, -10, 22],
 [0, 0, 0, 0, -26, -11, -8, 6, 3, -15],
 [0, 0, 0, 0, 0, -11, 27, 20, 12, 29],
 [0, 0, 0, 0, 0, 0, -4, -29, 26, -2],
 [0, 0, 0, 0, 0, 0, 0, 18, 17, -5],
 [0, 0, 0, 0, 0, 0, 0, 0, 20, -23],
 [0, 0, 0, 0, 0, 0, 0, 0, 0, 10]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute |A| for the matrix A =
[[-3, -18, 3, 15, -13, -7, -1, 19, -21, -29],
 [0, 24, -2, -30, -14, -9, 28, -5, 25, -21],
 [0, 0, -11, -9, 26, 21, 17, 25, -7, -9],
 [0, 0, 0, -29, 27, 11, 6, -27, 6, -10],
 [0, 0, 0, 0, 16, -16, -9, -30, 21, -5],
 [0, 0, 0, 0, 0, 26, -30, -19, 10, 30],
 [0, 0, 0, 0, 0, 0, 23, -12, -6, 8],
 [0, 0, 0, 0, 0, 0, 0, 23, -12, -22],
 [0, 0, 0, 0, 0, 0, 0, 0, 11, 1],
 [0, 0, 0, 0, 0, 0, 0, 0, 0, 27]]
Round to the nearest integer, then take the result modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the value of det(A) where A =
[[-24, 18, -25, 17, 30, -8, 9, -18, 26, -9],
 [0, -13, 2, 28, 28, -20, -24, 22, 9, 13],
 [0, 0, -30, 8, 18, -6, 3, -5, 13, 30],
 [0, 0, 0, -6, 29, 27, -25, 21, -4, -27],
 [0, 0, 0, 0, 11, 6, 19, -3, 5, -10],
 [0, 0, 0, 0, 0, 3, 16, 18, -7, 3],
 [0, 0, 0, 0, 0, 0, -21, 30, 12, -16],
 [0, 0, 0, 0, 0, 0, 0, -15, 2, 20],
 [0, 0, 0, 0, 0, 0, 0, 0, 29, 28],
 [0, 0, 0, 0, 0, 0, 0, 0, 0, -30]]
Round to the nearest integer, then give your answer as det(A) mod 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:
[[28, 28, 14, 22, 20, -24, 12, 27, -11, -21],
 [0, -16, -8, -21, -27, 2, -19, -22, -4, 27],
 [0, 0, -16, -24, -5, -23, -26, -29, -29, -21],
 [0, 0, 0, -15, -24, -19, -27, 22, 0, 1],
 [0, 0, 0, 0, -29, -20, 19, 29, -24, 16],
 [0, 0, 0, 0, 0, -13, -21, 19, 6, -19],
 [0, 0, 0, 0, 0, 0, -11, 21, 5, 4],
 [0, 0, 0, 0, 0, 0, 0, -18, 25, 9],
 [0, 0, 0, 0, 0, 0, 0, 0, -5, -29],
 [0, 0, 0, 0, 0, 0, 0, 0, 0, -2]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute |A| for the matrix A =
[[11, 29, 2, 5, -1, -8, 22, -28, 26, -22],
 [-28, 15, -22, -12, -9, -17, 19, 0, 17, 3],
 [23, 29, 22, 22, -8, 2, 23, 10, -3, -10],
 [-5, -21, -8, -28, -21, 14, 9, 28, -30, -3],
 [-18, 27, 8, 16, 23, 12, -17, 27, 7, -30],
 [-29, -25, -13, 21, 23, -13, -9, 16, -19, -20],
 [-22, 16, 23, -3, 11, 8, -12, -11, -27, -4],
 [-30, -4, 15, 10, 26, 24, 19, -3, 4, 8],
 [-30, 16, -28, -27, -4, 6, -8, -4, -6, -13],
 [30, 7, -29, -21, 13, 3, -5, -4, 1, 22]]
Round to the nearest integer, then take the result modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the value of det(A) where A =
[[6, -20, 18, -2, -18, -23, 30, -7, 29, -2],
 [-30, -18, 23, -6, 6, -24, -9, 2, 16, -16],
 [-28, 24, 30, -23, 8, 17, -30, -19, 0, -3],
 [-12, -13, 21, -18, 4, 26, 23, 7, -9, 26],
 [10, 10, -18, 5, 23, 10, 16, 16, -25, -23],
 [-7, 6, -15, -12, 7, 22, 15, 17, -28, -9],
 [5, -9, -8, -30, -9, -15, 25, 11, 15, -28],
 [-29, 30, 8, 30, -21, 5, 8, 26, 9, -15],
 [-18, 3, 11, -9, -12, -13, 17, -21, -12, -4],
 [14, 24, -17, -19, 14, -19, -9, -22, 4, 14]]
Round to the nearest integer, then give your answer as det(A) mod 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:
[[-6, 0, 6, -18, -11, -2, 0, -7, -28, 14],
 [0, 28, 30, 20, -25, 25, 4, -18, 27, 19],
 [0, 0, -18, 11, 22, 14, 25, 13, -3, -27],
 [0, 0, 0, 18, 6, -13, -29, 25, 19, 2],
 [0, 0, 0, 0, -15, 27, -1, -13, -4, 16],
 [0, 0, 0, 0, 0, -6, 2, 4, -7, 26],
 [0, 0, 0, 0, 0, 0, -18, 30, 3, -16],
 [0, 0, 0, 0, 0, 0, 0, 26, -23, 25],
 [0, 0, 0, 0, 0, 0, 0, 0, -23, -28],
 [0, 0, 0, 0, 0, 0, 0, 0, 0, -11]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute |A| for the matrix A =
[[12, 23, 2, -13, -9, 13, 10, 6, 15, -13],
 [0, -25, -3, -29, -16, 15, -20, -20, -5, -4],
 [0, 0, 25, -23, 23, 15, 28, -11, 3, -5],
 [0, 0, 0, 22, 10, -2, -20, -23, -1, -16],
 [0, 0, 0, 0, -20, 21, 17, 20, 15, -22],
 [0, 0, 0, 0, 0, 11, -8, -7, -12, -21],
 [0, 0, 0, 0, 0, 0, 11, 8, -18, 11],
 [0, 0, 0, 0, 0, 0, 0, -26, -20, 9],
 [0, 0, 0, 0, 0, 0, 0, 0, 3, -13],
 [0, 0, 0, 0, 0, 0, 0, 0, 0, -5]]
Round to the nearest integer, then take the result modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:
[[-11, -2, -1, 16, -10, 20, -17, 22, -3, -8],
 [-2, 5, 7, 28, 24, 4, 12, -22, 18, 14],
 [-1, 7, -15, 16, 12, 4, 4, -22, 2, 14],
 [16, 28, 16, 30, 8, 4, 14, -5, 2, 12],
 [-10, 24, 12, 8, -8, 8, 22, -14, -25, 24],
 [20, 4, 4, 4, 8, -16, -1, -8, 16, -12],
 [-17, 12, 4, 14, 22, -1, -14, -2, 18, 10],
 [22, -22, -22, -5, -14, -8, -2, 23, -16, -10],
 [-3, 18, 2, 2, -25, 16, 18, -16, 1, 16],
 [-8, 14, 14, 12, 24, -12, 10, -10, 16, 17]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute |A| for the matrix A =
[[-16, 20, -27, -21, -1, 8, 15, -19, 11, 8],
 [-23, 28, 30, -25, -14, -8, 19, -24, 2, 22],
 [-24, 1, 21, -2, -1, 25, -18, 23, 7, 16],
 [28, -13, -1, -10, 7, -1, -13, 3, -2, 18],
 [14, 20, -11, 0, 16, 5, -12, -18, -18, 14],
 [-25, 26, -8, -3, -30, 16, 24, 24, 19, -25],
 [8, 11, 25, 12, 25, 9, 2, 17, -10, -18],
 [-14, 0, -15, 17, 9, 14, 14, -14, -23, 11],
 [-6, 0, 24, -3, 21, 9, 7, -23, 17, 13],
 [20, 20, -29, -22, 19, -11, -27, 4, 29, 23]]
Round to the nearest integer, then take the result modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:
[[-25, 12, 4, -1, 14, -2, 12, -24, 12, -11],
 [12, 28, 8, -23, 22, -16, 0, 3, 16, -26],
 [4, 8, -27, -6, -19, -16, -2, -28, 8, 12],
 [-1, -23, -6, -13, 18, -4, -2, -6, -14, -8],
 [14, 22, -19, 18, 15, 0, 8, 26, -4, 0],
 [-2, -16, -16, -4, 0, 11, -6, -10, 23, -3],
 [12, 0, -2, -2, 8, -6, 27, 25, 2, -17],
 [-24, 3, -28, -6, 26, -10, 25, -28, -22, 10],
 [12, 16, 8, -14, -4, 23, 2, -22, 8, -2],
 [-11, -26, 12, -8, 0, -3, -17, 10, -2, 10]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:
[[-13, -6, -18, 29, -20, 6, -23, -4, -11, 25],
 [3, -27, -16, -18, 18, -9, -5, 19, 21, 30],
 [29, -22, -26, -1, -27, 0, -17, -6, 18, -3],
 [-16, 17, -28, 0, -18, -22, -29, -8, 17, 2],
 [-3, -23, 5, 28, -29, -7, -9, -16, -7, -26],
 [-4, 2, 22, -10, -14, 27, 4, 24, 24, -5],
 [15, -6, -10, 25, -20, -7, -17, -7, -22, -29],
 [-25, -6, -14, -28, -26, 1, 17, 24, -2, 5],
 [5, 30, 24, 30, -6, 25, -3, 29, 4, 21],
 [-18, -16, 18, 29, -4, -20, -25, 25, -4, 11]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:
[[-9, 9, 28, 19, -18, 1, -22, 6, 11, 8],
 [0, 3, -21, -7, -21, 14, -5, 3, 6, -27],
 [0, 0, -6, -20, 15, 24, -11, -7, 16, 0],
 [0, 0, 0, 13, 26, -8, 25, 22, -14, -29],
 [0, 0, 0, 0, -14, 22, 26, 2, 27, 30],
 [0, 0, 0, 0, 0, -11, -3, 27, -19, -11],
 [0, 0, 0, 0, 0, 0, -20, 10, -20, 1],
 [0, 0, 0, 0, 0, 0, 0, -7, 13, 30],
 [0, 0, 0, 0, 0, 0, 0, 0, 12, 5],
 [0, 0, 0, 0, 0, 0, 0, 0, 0, -13]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the determinant of the matrix:
[[-14, -6, 18, 6, -14, -4, 0, -17, 22, 5],
 [-9, 25, 26, -26, 9, -25, 9, -26, -7, -9],
 [-17, -6, -11, -30, 18, 4, 6, 27, 21, -3],
 [-2, 27, 27, 9, -23, -13, 0, -10, -25, -22],
 [-1, 13, -13, -1, 26, -11, 29, 24, 28, -21],
 [25, -18, 10, -29, 24, -26, 2, -30, 25, 6],
 [30, 27, -19, 10, -3, -13, 5, -1, 11, 23],
 [23, 7, -10, 8, 28, -24, -26, 27, 4, -16],
 [-22, 17, 24, -13, 20, -19, -4, -17, 26, -18],
 [-1, 5, 22, 18, 21, 10, -22, 3, -19, 19]]? Round to the nearest integer, then express your answer modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the value of det(A) where A =
[[21, 19, 15, 3, -21, -12, 28, 8, -20, 9],
 [9, 5, -8, 24, 13, 7, -6, 13, 18, 14],
 [-10, 7, -4, -29, -25, 4, -22, -11, 24, 21],
 [2, 16, -2, -4, -30, -18, -28, -30, -11, 9],
 [27, -5, -19, -25, 23, 19, -22, 25, 24, 5],
 [-11, -21, -21, 0, -11, -6, 14, 0, 16, 10],
 [-22, 22, 10, 18, -7, -27, 6, 14, -7, -17],
 [-23, 18, -4, 30, 11, 22, -1, 19, -17, 9],
 [9, 27, -13, -18, -2, -3, 17, 21, 19, -27],
 [-4, 5, -7, 27, 26, -7, -28, 14, -12, 8]]
Round to the nearest integer, then give your answer as det(A) mod 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:
[[24, 18, -20, 25, 24, 11, 21, 16, -18, -5],
 [-1, -11, -23, 27, 12, -11, 15, -20, -3, -20],
 [-22, 5, -4, -25, -3, -18, 14, -8, 16, -20],
 [24, -10, 8, -7, -20, 14, -5, 17, 11, -11],
 [28, -2, -27, 19, -13, 28, 15, 27, 29, -19],
 [1, 29, 0, -23, -6, -20, -5, 10, 29, -12],
 [17, -14, -21, 3, 25, -2, 20, 14, -3, -13],
 [1, 5, -26, -13, -15, -28, -25, 2, 29, -15],
 [13, -29, 24, -29, -26, -3, 21, 29, -30, 29],
 [-26, -27, 25, -2, -29, -16, -26, 29, 28, 0]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the determinant of the matrix:
[[-10, 7, 17, 2, -15, -28, 25, -28, 4, -8],
 [0, -7, 6, 30, 24, -18, -16, -24, -7, 19],
 [0, 0, 22, -12, -28, -26, 19, 6, 12, 21],
 [0, 0, 0, 18, -11, -15, 13, 17, -24, 3],
 [0, 0, 0, 0, -21, 11, 13, -23, -10, 14],
 [0, 0, 0, 0, 0, 12, -2, 29, -11, -14],
 [0, 0, 0, 0, 0, 0, 27, -25, -14, 25],
 [0, 0, 0, 0, 0, 0, 0, -9, 12, 18],
 [0, 0, 0, 0, 0, 0, 0, 0, 4, -29],
 [0, 0, 0, 0, 0, 0, 0, 0, 0, 6]]? Round to the nearest integer, then express your answer modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:
[[-12, -3, -5, 25, -6, 14, 30, 17, 14, 13],
 [0, 15, 10, -4, 8, -11, 0, -19, -6, 3],
 [0, 0, 12, 18, 4, 24, 9, 8, 17, 27],
 [0, 0, 0, -5, -4, 3, -10, -24, 1, -25],
 [0, 0, 0, 0, -28, 17, -9, -15, 8, -11],
 [0, 0, 0, 0, 0, -11, -3, 19, -24, -26],
 [0, 0, 0, 0, 0, 0, 13, -21, -13, 21],
 [0, 0, 0, 0, 0, 0, 0, 16, -19, 3],
 [0, 0, 0, 0, 0, 0, 0, 0, 15, -3],
 [0, 0, 0, 0, 0, 0, 0, 0, 0, 14]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the value of det(A) where A =
[[11, 12, 0, -22, -12, -8, 14, -3, -6, 16],
 [12, -8, 15, 16, -16, -3, 0, 16, 6, -16],
 [0, 15, 4, 18, 4, 14, -6, 6, 5, 1],
 [-22, 16, 18, 30, 2, 4, 12, -3, 8, 12],
 [-12, -16, 4, 2, -8, 22, 2, 13, 10, -4],
 [-8, -3, 14, 4, 22, -15, -6, -10, 18, 0],
 [14, 0, -6, 12, 2, -6, -30, -18, 2, -5],
 [-3, 16, 6, -3, 13, -10, -18, 29, 8, 0],
 [-6, 6, 5, 8, 10, 18, 2, 8, 20, 20],
 [16, -16, 1, 12, -4, 0, -5, 0, 20, -5]]
Round to the nearest integer, then give your answer as det(A) mod 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the determinant of the matrix:
[[-13, 12, -14, -19, 30, 5, -7, -10, 14, 27],
 [0, -14, -30, -20, -16, 14, -19, 8, -25, 11],
 [0, 0, -10, 13, -30, -8, -12, 3, -19, 23],
 [0, 0, 0, -23, 7, -21, 12, -17, -12, -23],
 [0, 0, 0, 0, 25, -21, -2, 2, 17, -16],
 [0, 0, 0, 0, 0, 25, -25, -10, 30, 13],
 [0, 0, 0, 0, 0, 0, -9, -29, -30, 6],
 [0, 0, 0, 0, 0, 0, 0, -9, 25, -9],
 [0, 0, 0, 0, 0, 0, 0, 0, 16, -10],
 [0, 0, 0, 0, 0, 0, 0, 0, 0, -29]]? Round to the nearest integer, then express your answer modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the value of det(A) where A =
[[13, -11, 15, -26, 12, -6, -13, 5, 25, -15],
 [-28, 19, -12, 17, 8, -1, -22, 22, 27, -29],
 [12, 15, 28, -8, 4, -24, -25, -30, 15, 11],
 [-2, -26, -18, 28, -16, -30, -8, 12, 23, -18],
 [10, -20, -19, 0, -11, -22, -10, -18, -26, 6],
 [-2, -1, 11, 6, -20, 24, 1, 18, -1, -5],
 [24, 8, -26, 4, 8, -26, -27, 10, 21, -26],
 [-19, -25, -1, 12, 7, 19, 12, 20, -23, -22],
 [-25, -14, 13, 14, -3, 3, -2, -12, -4, -13],
 [-26, 27, -25, -11, -5, 18, -5, 17, -24, 30]]
Round to the nearest integer, then give your answer as det(A) mod 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:
[[-3, 17, -20, -14, -15, -7, 2, 27, 18, 11],
 [0, -29, 26, 19, -5, 29, -2, -19, -28, -13],
 [0, 0, 9, 19, -1, 8, 11, 4, 18, -22],
 [0, 0, 0, 24, 10, 19, 18, -11, 17, -14],
 [0, 0, 0, 0, -16, 25, -24, 30, 3, 9],
 [0, 0, 0, 0, 0, 18, 20, 11, -29, -23],
 [0, 0, 0, 0, 0, 0, -11, 0, 19, -14],
 [0, 0, 0, 0, 0, 0, 0, -28, 14, 28],
 [0, 0, 0, 0, 0, 0, 0, 0, 5, -11],
 [0, 0, 0, 0, 0, 0, 0, 0, 0, 9]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute |A| for the matrix A =
[[-18, 23, -6, -10, -18, -10, -16, 0, -26, -10],
 [0, -22, 29, 19, 14, -22, -22, -22, -17, 27],
 [0, 0, 27, -27, 12, -1, -19, 6, -2, -15],
 [0, 0, 0, -16, 29, 15, 2, -23, 10, -3],
 [0, 0, 0, 0, 10, -18, 28, 2, -9, 11],
 [0, 0, 0, 0, 0, 17, 22, -6, -5, -6],
 [0, 0, 0, 0, 0, 0, -21, 30, 0, -29],
 [0, 0, 0, 0, 0, 0, 0, -19, -2, 3],
 [0, 0, 0, 0, 0, 0, 0, 0, 28, -9],
 [0, 0, 0, 0, 0, 0, 0, 0, 0, -30]]
Round to the nearest integer, then take the result modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute |A| for the matrix A =
[[-18, 12, -27, -16, 13, -16, 6, 24, -5, -14],
 [12, -23, 10, 14, -21, 19, -13, 2, 8, -26],
 [-27, 10, 23, 6, 22, -25, 3, 16, 8, 12],
 [-16, 14, 6, 14, -12, -17, 20, 12, 8, -4],
 [13, -21, 22, -12, 22, -16, 8, 24, 10, -4],
 [-16, 19, -25, -17, -16, 15, 10, 26, 12, 6],
 [6, -13, 3, 20, 8, 10, 11, 5, 4, -2],
 [24, 2, 16, 12, 24, 26, 5, 3, 4, -10],
 [-5, 8, 8, 8, 10, 12, 4, 4, -27, 7],
 [-14, -26, 12, -4, -4, 6, -2, -10, 7, -26]]
Round to the nearest integer, then take the result modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the value of det(A) where A =
[[27, -12, -12, 6, 10, 6, -12, -12, -4, 10],
 [-12, -7, -23, -6, -8, 14, 18, 4, 10, 9],
 [-12, -23, -13, -20, -6, -15, -8, 26, 0, 0],
 [6, -6, -20, -14, -19, -6, 22, 18, -10, 24],
 [10, -8, -6, -19, 23, -10, 5, -6, 12, -12],
 [6, 14, -15, -6, -10, 21, -17, 14, -5, 6],
 [-12, 18, -8, 22, 5, -17, 13, 11, 10, -16],
 [-12, 4, 26, 18, -6, 14, 11, -1, 4, -1],
 [-4, 10, 0, -10, 12, -5, 10, 4, 14, 11],
 [10, 9, 0, 24, -12, 6, -16, -1, 11, 19]]
Round to the nearest integer, then give your answer as det(A) mod 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:
[[-5, -9, 12, -4, 4, 1, 20, 4, -10, -7],
 [-9, -18, 10, -24, 28, -10, 16, 1, 16, 10],
 [12, 10, -25, -3, 22, -20, -14, -8, 6, -13],
 [-4, -24, -3, -21, 2, 1, 9, 25, 4, 3],
 [4, 28, 22, 2, 6, -20, 19, 12, 0, 8],
 [1, -10, -20, 1, -20, 10, -5, 4, 2, -24],
 [20, 16, -14, 9, 19, -5, 8, 16, 21, -16],
 [4, 1, -8, 25, 12, 4, 16, 18, -12, 13],
 [-10, 16, 6, 4, 0, 2, 21, -12, -28, 5],
 [-7, 10, -13, 3, 8, -24, -16, 13, 5, 13]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:
[[-1, -5, 4, 13, 30, -30, 0, -1, -12, 28],
 [-2, 27, 29, -5, -8, 22, -8, 6, -12, 8],
 [1, -3, -28, -12, -7, 25, -4, -9, -23, -14],
 [-17, 0, 20, 29, -13, 30, -9, -24, -4, 6],
 [20, -14, 18, 4, 14, -28, -29, -28, -10, 28],
 [6, -20, 28, -30, 29, -12, -10, 21, -3, -13],
 [-21, 12, 6, -12, 22, -17, 29, -30, -4, -19],
 [12, 24, 6, 12, -6, -24, 12, 29, 17, -1],
 [-3, -23, -8, -19, -6, -22, 15, 1, -14, 19],
 [7, 9, 13, -27, 26, 19, 7, -1, -7, -29]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute |A| for the matrix A =
[[18, 8, 27, -22, -7, -7, -16, -24, 25, 25],
 [-11, 20, 29, 5, -16, 14, 9, 13, -8, -26],
 [-13, -22, 11, -9, 3, 28, -30, 23, 12, -1],
 [-12, -28, -3, -21, -22, -3, -20, -15, -8, 4],
 [23, -20, -7, 4, 22, -10, -17, -4, 14, -30],
 [-4, 14, 6, -5, 19, 26, 7, 28, 19, -20],
 [27, 23, 16, -20, -26, -26, -15, -17, 25, 2],
 [21, -7, -26, 11, 15, 0, 20, 4, -14, 30],
 [-19, 13, 5, 8, -24, 29, -17, 25, -15, 0],
 [16, -10, 14, 5, 20, 12, -9, 12, -5, 22]]
Round to the nearest integer, then take the result modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the value of det(A) where A =
[[-3, -27, -4, 15, -29, 12, 5, 24, 7, 5],
 [-26, -3, -22, 30, -17, -10, 27, 25, 29, -19],
 [22, 20, 16, 10, -16, 16, -3, -20, -11, -4],
 [1, 26, 18, 26, 18, 25, 19, -18, -27, 17],
 [29, -17, -25, -28, -1, 11, -19, -25, -6, 29],
 [-4, 21, 4, 18, 4, 29, -24, -11, 12, -21],
 [-20, 29, 10, -24, -15, -28, -6, -8, -3, 21],
 [-10, -27, 25, 20, 12, 14, 12, -23, 19, -1],
 [5, 29, 0, 1, 6, 5, 19, 5, 28, 7],
 [21, 3, -1, -4, 20, -23, 3, -16, 22, -2]]
Round to the nearest integer, then give your answer as det(A) mod 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:
[[-23, -3, 27, 7, -24, 21, -2, -2, -1, 12],
 [0, 11, 14, 1, -12, 23, 19, -25, 12, 11],
 [0, 0, 7, -24, -13, 0, -26, 29, -25, -12],
 [0, 0, 0, -21, 17, 9, -3, 20, 9, -21],
 [0, 0, 0, 0, -5, 30, -4, -21, 19, 7],
 [0, 0, 0, 0, 0, 10, 16, -23, -8, 9],
 [0, 0, 0, 0, 0, 0, 24, 9, -19, 13],
 [0, 0, 0, 0, 0, 0, 0, -5, 7, -15],
 [0, 0, 0, 0, 0, 0, 0, 0, -12, 9],
 [0, 0, 0, 0, 0, 0, 0, 0, 0, -13]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:
[[-29, -22, -1, -6, 0, -2, -17, -3, -23, 8],
 [0, 6, -4, 22, -22, -18, 10, -11, 25, -15],
 [0, 0, -28, -16, -30, 18, 25, -16, 25, -15],
 [0, 0, 0, -12, -21, -23, -11, 26, -22, -24],
 [0, 0, 0, 0, -8, 8, 10, 5, -5, 9],
 [0, 0, 0, 0, 0, 11, 2, 20, 13, 5],
 [0, 0, 0, 0, 0, 0, -13, -1, 26, -12],
 [0, 0, 0, 0, 0, 0, 0, 16, 8, 19],
 [0, 0, 0, 0, 0, 0, 0, 0, -8, 0],
 [0, 0, 0, 0, 0, 0, 0, 0, 0, 3]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:
[[-29, -18, -21, -6, 2, 10, -4, -2, 26, 21],
 [-4, 8, -15, 22, 12, -2, 4, 15, -15, -16],
 [-4, 2, -6, 2, -19, -17, -21, 11, 6, -19],
 [30, 16, -10, 5, -24, -19, -11, 3, 0, -25],
 [14, 11, -27, -15, 9, -1, 1, -3, -28, 17],
 [28, 19, -28, -4, 25, 20, 10, -2, 14, -18],
 [14, 16, 21, -20, -23, 13, 6, -2, -21, 24],
 [24, 16, 8, -24, -23, 7, -5, -29, 5, 4],
 [-20, 19, -7, -2, 22, -8, -26, -7, -17, -14],
 [8, 13, -30, 25, -19, 7, 22, 13, -15, 5]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:
[[-30, 14, 21, -18, 2, 12, -7, -20, -26, 12],
 [0, 1, 4, 21, 20, -12, 30, -30, -16, -12],
 [0, 0, 15, 5, -23, 14, 18, -5, 5, -13],
 [0, 0, 0, -26, 23, 5, 20, -3, -14, -17],
 [0, 0, 0, 0, -28, -28, -12, 24, 2, 5],
 [0, 0, 0, 0, 0, -7, -2, 9, 14, -4],
 [0, 0, 0, 0, 0, 0, -27, 6, 3, -24],
 [0, 0, 0, 0, 0, 0, 0, -11, 26, 24],
 [0, 0, 0, 0, 0, 0, 0, 0, -5, 29],
 [0, 0, 0, 0, 0, 0, 0, 0, 0, 3]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:
[[-14, -28, 24, 2, -22, -25, -22, -13, 9, -23],
 [-14, 24, -6, -6, 22, -22, 28, -22, -27, -16],
 [-21, -16, -14, 7, 6, -28, -12, 30, -10, 23],
 [23, 8, -30, -7, -13, -14, 1, -2, 17, -29],
 [10, -28, 29, -24, -9, 7, -23, 4, -27, 12],
 [12, -10, 6, 23, -16, 14, -3, 27, 11, 16],
 [-26, 2, 29, -27, -26, 14, 22, -28, 29, 24],
 [-10, -25, -20, -6, -23, 22, -3, 21, -30, 22],
 [21, -5, 1, -27, 16, -7, 12, 3, 16, -7],
 [16, 0, 27, -22, 18, 27, 20, -16, -2, -21]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute |A| for the matrix A =
[[0, 2, 12, 21, -29, -2, -23, -27, -30, 28],
 [-30, 16, -2, 13, 7, -6, -13, -19, -20, -26],
 [30, -24, 28, 22, 6, 12, 30, 4, 22, 2],
 [-22, -14, 29, 16, 16, -28, 9, -14, 8, -18],
 [-28, -12, 6, 15, -25, 3, 4, 8, -17, 23],
 [-19, -3, 8, -29, 8, 18, 7, -6, -4, 30],
 [25, 28, 3, 26, -3, 12, 11, 15, -4, -22],
 [-2, -23, 23, 21, 8, -29, 25, -14, 8, 7],
 [5, -17, -8, -30, -30, -28, 9, -8, -3, -15],
 [-2, 2, 1, 24, 16, -8, 16, 16, 30, 15]]
Round to the nearest integer, then take the result modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the value of det(A) where A =
[[-19, 4, 23, -9, 22, 26, -2, -12, -13, 25],
 [-13, 13, 30, 16, 18, -15, 13, 27, 28, 25],
 [-12, 18, 21, -22, 2, 25, -18, -20, 30, 2],
 [6, -1, 8, 15, -22, -8, -7, 1, 18, 7],
 [-27, 13, 10, 15, -4, -20, -10, -17, -13, 28],
 [30, -7, -11, 10, -5, 0, 21, -15, 10, 17],
 [11, 8, -12, -24, 21, -15, -7, -25, 9, -15],
 [26, 5, 8, -16, 9, 19, -27, 25, -29, -17],
 [29, -9, -29, -11, -27, 21, 3, -13, 19, 17],
 [24, 16, 18, -11, -5, -24, 23, -12, -7, -20]]
Round to the nearest integer, then give your answer as det(A) mod 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute |A| for the matrix A =
[[-15, -30, 5, -3, -18, -20, 23, -25, 28, -1],
 [21, 27, 6, 3, 19, -3, -22, 0, -25, 29],
 [27, -25, 5, -11, 9, 1, 16, 18, 1, -26],
 [7, 6, -21, 6, 16, -29, -24, -20, -30, -17],
 [-10, -25, 17, -5, -14, -5, -24, 17, -30, -16],
 [0, 5, -25, -12, -25, -1, 4, 14, 26, -14],
 [-15, -21, 5, 14, -13, -21, 21, 6, -27, 29],
 [-23, -7, 16, 3, -19, -7, 27, 11, 13, -4],
 [26, 7, 21, -14, 19, -15, 16, 10, -4, 4],
 [18, -5, 17, 23, -25, 14, 15, -30, 5, -12]]
Round to the nearest integer, then take the result modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the determinant of the matrix:
[[17, -1, 2, -14, 20, 8, 6, 8, 13, -22],
 [0, -27, 13, 24, -14, -27, 13, 17, 27, 10],
 [0, 0, -21, 14, 16, -10, 25, 25, 1, -1],
 [0, 0, 0, -11, 9, 25, 23, 18, -3, -22],
 [0, 0, 0, 0, 23, -11, -25, 20, -6, 6],
 [0, 0, 0, 0, 0, -26, 25, 6, 21, -30],
 [0, 0, 0, 0, 0, 0, -25, 26, 12, -4],
 [0, 0, 0, 0, 0, 0, 0, -26, 16, -11],
 [0, 0, 0, 0, 0, 0, 0, 0, -23, 19],
 [0, 0, 0, 0, 0, 0, 0, 0, 0, 19]]? Round to the nearest integer, then express your answer modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the value of det(A) where A =
[[-23, 25, -17, -14, -20, -25, 0, -19, 10, 20],
 [7, -4, 27, -26, -2, 18, -1, -18, -18, 29],
 [26, 25, 26, -2, 14, -26, -17, -9, 20, -14],
 [-12, 15, 22, 14, 10, 23, 5, 17, 24, -19],
 [-6, 24, -8, -14, 4, 8, -7, 7, 9, 24],
 [-19, 27, 12, 7, 27, -17, -17, -21, 16, -30],
 [-8, 29, -3, -24, 30, 1, 12, -20, -22, -7],
 [9, -27, -14, 28, -10, -6, 2, -28, -27, 12],
 [-18, 23, 29, -2, 20, 5, -25, 4, -17, -30],
 [-24, 0, 17, 7, 10, 13, -11, -2, -4, -9]]
Round to the nearest integer, then give your answer as det(A) mod 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the value of det(A) where A =
[[29, -30, 17, 0, -1, -19, -17, 6, -25, 29],
 [-1, 27, -14, 24, -18, 27, 17, 7, -15, 17],
 [26, -3, -19, 5, -15, -19, -30, -12, -25, -25],
 [-13, 17, -3, -19, 0, -4, 15, 18, -23, -20],
 [-24, 29, -9, -11, -12, -29, 18, 14, -4, 25],
 [-6, 15, -20, -22, 27, -5, 0, 10, 18, 18],
 [25, -20, -19, 30, 12, -21, -5, -22, -13, -6],
 [-13, 12, 18, 29, 13, 23, 30, -17, -4, -9],
 [28, 5, -14, -19, -17, -25, -21, 12, 14, -17],
 [-9, 14, -28, -23, 7, 22, 5, -26, 3, -30]]
Round to the nearest integer, then give your answer as det(A) mod 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the determinant of the matrix:
[[4, 14, -27, -15, 28, 19, 9, 1, -7, -11],
 [0, 8, 23, -28, -23, 3, -17, -11, -10, 6],
 [0, 0, -5, -12, 20, -14, 1, -28, 25, -7],
 [0, 0, 0, -18, -6, -1, 8, -18, 1, 17],
 [0, 0, 0, 0, -26, -4, 22, -21, 30, 21],
 [0, 0, 0, 0, 0, -27, -21, -30, -28, -10],
 [0, 0, 0, 0, 0, 0, -11, -11, 7, 9],
 [0, 0, 0, 0, 0, 0, 0, -29, -27, -14],
 [0, 0, 0, 0, 0, 0, 0, 0, -10, -11],
 [0, 0, 0, 0, 0, 0, 0, 0, 0, -23]]? Round to the nearest integer, then express your answer modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the determinant of the matrix:
[[7, 30, 25, 20, -26, 15, 26, -25, -30, -11],
 [-4, 2, -10, -20, 15, -30, 12, 19, -17, -12],
 [-28, -16, -2, 22, 23, 17, -30, -13, -1, -21],
 [-4, -28, -15, -21, 26, -23, 12, -3, 25, 8],
 [30, 22, 27, -2, 10, -18, 18, -5, 18, 25],
 [27, 26, -27, 3, -13, -9, -20, -22, 3, 10],
 [-13, -9, 10, -21, -3, -8, -28, 28, -24, -23],
 [1, 30, 13, -30, 29, -6, -5, 4, -18, -3],
 [-20, 23, -19, 20, 28, 12, -3, -6, -2, 23],
 [28, 21, -30, 9, -8, 20, -6, -14, -24, 11]]? Round to the nearest integer, then express your answer modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:
[[27, 0, -26, -10, -9, -16, -6, -12, 2, 25],
 [0, 15, 12, 4, -4, 10, -4, -19, 8, -18],
 [-26, 12, 29, -8, -15, -8, -26, -3, 15, 12],
 [-10, 4, -8, -24, 0, 0, -13, 13, 14, -18],
 [-9, -4, -15, 0, -26, 20, 30, -22, 20, 12],
 [-16, 10, -8, 0, 20, 15, 24, -12, 5, -6],
 [-6, -4, -26, -13, 30, 24, -20, 6, 6, 2],
 [-12, -19, -3, 13, -22, -12, 6, -11, 1, -12],
 [2, 8, 15, 14, 20, 5, 6, 1, -3, -24],
 [25, -18, 12, -18, 12, -6, 2, -12, -24, -22]]

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[User]
Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:
[[-5, 1, -28, -13, -10, 0, -7, 3, 11, -26],
 [1, -10, 15, -4, 2, -28, -12, 26, -30, 14],
 [25, -27, 27, -4, 24, 22, 11, -8, -27, -11],
 [-19, 0, -22, -18, 3, 2, 9, 23, 15, -1],
 [16, 28, 15, -9, -24, 20, 5, -14, -22, 12],
 [-27, 7, 24, -3, 1, -13, -26, 22, -29, -20],
 [-1, 13, -4, 17, -16, -7, -12, 9, 23, -30],
 [21, -3, -23, -9, 29, -6, 28, -13, -22, -23],
 [12, 22, -9, 26, -29, 30, 26, 6, 4, -25],
 [-20, -8, 12, -16, 24, -12, 20, 11, -7, -21]]

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[User]
What is the determinant of the matrix:
[[17, 7, -27, -28, 10, -6, -27, -14, -28, -14],
 [0, -27, -25, -2, 5, -17, 30, 21, 18, 1],
 [0, 0, 16, -26, 20, -30, -9, -11, 20, 29],
 [0, 0, 0, 14, 25, 30, 26, 22, 21, -28],
 [0, 0, 0, 0, 29, -19, 19, 30, -12, -22],
 [0, 0, 0, 0, 0, 1, 14, 8, -20, -18],
 [0, 0, 0, 0, 0, 0, 9, -25, 15, -12],
 [0, 0, 0, 0, 0, 0, 0, -9, 17, -13],
 [0, 0, 0, 0, 0, 0, 0, 0, 15, 8],
 [0, 0, 0, 0, 0, 0, 0, 0, 0, 26]]? Round to the nearest integer, then express your answer modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the determinant of the matrix:
[[-6, 0, -12, -12, -7, -8, -18, 25, -18, 0],
 [0, 16, -12, 6, 6, -18, -10, -16, -2, 16],
 [-12, -12, -19, -10, 12, -20, 14, 21, -24, 9],
 [-12, 6, -10, -3, 3, -4, 12, 8, 4, 9],
 [-7, 6, 12, 3, -10, -16, -6, -21, 24, -6],
 [-8, -18, -20, -4, -16, 21, -6, -24, -10, -20],
 [-18, -10, 14, 12, -6, -6, -10, 16, -4, -3],
 [25, -16, 21, 8, -21, -24, 16, 9, -8, -26],
 [-18, -2, -24, 4, 24, -10, -4, -8, -14, -8],
 [0, 16, 9, 9, -6, -20, -3, -26, -8, 8]]? Round to the nearest integer, then express your answer modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the determinant of the matrix:
[[-19, -4, 10, 17, -4, -8, 1, 22, 4, 4],
 [-4, 26, 2, 0, 18, -2, -6, -14, 0, 30],
 [10, 2, -18, 10, 24, 14, -4, 8, -20, -1],
 [17, 0, 10, -8, 2, -4, 15, 4, -4, 15],
 [-4, 18, 24, 2, 24, -16, 8, 20, -18, -18],
 [-8, -2, 14, -4, -16, -10, -14, -8, 8, -4],
 [1, -6, -4, 15, 8, -14, 18, -16, 18, -9],
 [22, -14, 8, 4, 20, -8, -16, 30, 15, 2],
 [4, 0, -20, -4, -18, 8, 18, 15, 8, 10],
 [4, 30, -1, 15, -18, -4, -9, 2, 10, -21]]? Round to the nearest integer, then express your answer modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:
[[16, -29, 6, -19, -9, 29, -27, 10, -16, 15],
 [0, 1, 0, 4, 12, 18, -7, 18, 27, -3],
 [0, 0, 9, -25, -5, 10, -15, -17, -2, -8],
 [0, 0, 0, 1, 4, -30, 12, 28, -18, -24],
 [0, 0, 0, 0, -17, -5, 20, -14, -2, 23],
 [0, 0, 0, 0, 0, -29, 17, 24, 19, 28],
 [0, 0, 0, 0, 0, 0, -24, 9, -4, 3],
 [0, 0, 0, 0, 0, 0, 0, 26, 2, -19],
 [0, 0, 0, 0, 0, 0, 0, 0, 11, 7],
 [0, 0, 0, 0, 0, 0, 0, 0, 0, -19]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:
[[-1, -19, -30, 29, 26, 24, -13, -15, 17, -6],
 [0, 21, -18, 23, 9, 5, -10, -24, -26, -11],
 [0, 0, -29, -14, 10, -28, 1, -5, -22, 7],
 [0, 0, 0, 8, -11, -3, -3, 19, -6, -5],
 [0, 0, 0, 0, 20, -7, 9, -27, 26, 23],
 [0, 0, 0, 0, 0, -12, -8, 17, -25, 6],
 [0, 0, 0, 0, 0, 0, 15, 0, 8, 28],
 [0, 0, 0, 0, 0, 0, 0, 14, 27, 24],
 [0, 0, 0, 0, 0, 0, 0, 0, -3, 2],
 [0, 0, 0, 0, 0, 0, 0, 0, 0, -30]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the determinant of the matrix:
[[15, -16, -6, -28, -11, -18, 16, -28, 23, 0],
 [18, -22, -4, -13, 17, 0, 19, 5, -30, -1],
 [20, 15, 11, -25, 29, 2, -4, 29, 6, -26],
 [-27, -16, -17, 19, 5, -29, 11, 20, 16, 18],
 [-12, 2, -23, 18, 28, -30, -21, -18, -8, -29],
 [15, -27, -30, 23, 20, 14, -12, 26, 30, -24],
 [26, -22, -6, 24, -27, 6, -17, -9, -19, 17],
 [-21, -3, -21, 14, 28, 30, 17, 9, 3, -24],
 [-26, -10, -24, 29, -30, 2, -6, 21, 13, 11],
 [-7, 11, -23, -1, -17, -1, -22, -7, -30, -11]]? Round to the nearest integer, then express your answer modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute |A| for the matrix A =
[[-9, 5, -30, -15, 6, 8, -1, 21, -20, -19],
 [0, -12, -7, -6, 17, -15, 3, 17, -13, -2],
 [0, 0, 23, -20, 0, -20, 6, 18, -21, 23],
 [0, 0, 0, 11, -17, 12, -29, 22, 19, -2],
 [0, 0, 0, 0, 10, 3, -19, -2, -25, -5],
 [0, 0, 0, 0, 0, -19, -22, 17, 10, -2],
 [0, 0, 0, 0, 0, 0, 25, -19, 29, 1],
 [0, 0, 0, 0, 0, 0, 0, 4, -2, -7],
 [0, 0, 0, 0, 0, 0, 0, 0, 23, 3],
 [0, 0, 0, 0, 0, 0, 0, 0, 0, -4]]
Round to the nearest integer, then take the result modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:
[[-9, -29, 22, -5, -20, 7, 25, 21, 15, 17],
 [-28, 1, 12, -11, 11, 8, -11, -23, 20, -8],
 [-9, -1, 18, -6, -10, 6, -28, -7, -9, 11],
 [-11, 27, -29, -27, -14, 18, 15, -3, 9, -11],
 [16, 26, 17, -25, -5, 21, -22, 29, 0, 0],
 [27, 18, -27, -3, -8, -28, -4, 27, 7, 11],
 [-27, 10, 11, -11, -27, 27, 10, -13, 19, 15],
 [-11, -13, 0, -18, 19, -25, -11, 11, -15, -28],
 [5, -8, 24, 4, -4, -6, -5, 19, 19, 4],
 [-2, 7, -1, -18, 7, -24, -18, 8, -30, 1]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:
[[25, -29, 15, -17, -22, -13, -20, -14, -4, 23],
 [-26, 5, 3, 23, -4, -13, 22, 10, -30, -15],
 [14, 29, 8, 19, -12, 13, 2, -1, -4, 1],
 [-2, -23, 13, 11, 4, 4, 26, -17, 6, 7],
 [9, 9, 7, 24, 1, 18, -21, 21, -2, 0],
 [23, 13, -23, -8, 27, 28, -25, 16, -10, -26],
 [6, -26, -25, -26, 22, -30, 20, 18, -4, -19],
 [17, -28, 18, 23, -25, 23, 24, 27, -30, -21],
 [-21, -23, -19, 21, -6, 19, 3, -7, -30, -27],
 [-18, -8, 13, -20, 5, 10, -12, -26, -12, -28]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the determinant of the matrix:
[[19, -4, 3, -2, 21, 21, 28, 10, -13, -21],
 [0, 24, 15, 18, 6, 23, -26, -15, 21, 27],
 [0, 0, 1, 14, 30, -3, 3, -4, 19, 9],
 [0, 0, 0, -12, 17, 18, 19, 19, -9, -8],
 [0, 0, 0, 0, -28, -26, -1, -22, -17, -30],
 [0, 0, 0, 0, 0, 27, 3, -4, -12, 4],
 [0, 0, 0, 0, 0, 0, 11, 7, -23, 0],
 [0, 0, 0, 0, 0, 0, 0, -24, 21, -17],
 [0, 0, 0, 0, 0, 0, 0, 0, -16, 28],
 [0, 0, 0, 0, 0, 0, 0, 0, 0, -16]]? Round to the nearest integer, then express your answer modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the determinant of the matrix:
[[-16, -8, -6, -11, -16, 15, -28, 12, 27, 18],
 [19, 10, 29, -24, 12, -30, -18, -18, 24, -15],
 [5, 19, 7, 27, -4, -9, 30, -23, -15, 1],
 [30, -15, 6, 22, -25, -6, 27, 11, -8, -12],
 [-6, -30, -22, 1, 14, 23, 19, -14, -18, -7],
 [21, -1, 12, 9, 24, -10, 13, 5, -17, 21],
 [-8, -15, -7, -17, 25, 24, 2, 18, -14, 15],
 [28, 4, -28, 2, -3, -3, -26, -23, 14, 19],
 [-24, 28, 4, -21, -13, -25, 27, 6, 27, 30],
 [25, -15, 24, 8, 0, 18, 7, 15, 23, 6]]? Round to the nearest integer, then express your answer modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute |A| for the matrix A =
[[10, 11, -30, 2, 5, 10, 3, 9, -24, -8],
 [-13, -30, -20, 21, -11, 19, -11, 1, 29, 1],
 [20, -11, -4, 10, -27, 2, 18, -10, -8, 4],
 [20, 28, -26, -25, 1, 28, -25, 11, -5, 28],
 [-22, -30, -10, -9, -7, 6, 28, -10, -16, -21],
 [-5, 25, -21, 12, -5, -24, -22, 25, -18, 1],
 [21, 5, -7, -14, 8, -29, 1, 19, -25, 16],
 [13, 26, -5, 11, -13, -15, -26, 22, 4, 29],
 [2, -11, 12, -27, 22, 3, 3, 27, -24, 20],
 [3, 1, -5, -2, -13, 7, -6, 12, -3, -30]]
Round to the nearest integer, then take the result modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:
[[-27, 3, -6, 0, 1, -6, 5, -8, 10, -3],
 [3, 6, 22, -24, 1, -17, -22, 4, 12, 6],
 [-6, 22, -11, 0, -6, -14, 11, 8, -12, 19],
 [0, -24, 0, 21, 3, -6, -8, 6, -2, 22],
 [1, 1, -6, 3, 24, -8, 12, -7, 12, -14],
 [-6, -17, -14, -6, -8, 16, 6, 23, -11, 10],
 [5, -22, 11, -8, 12, 6, -23, 13, 2, -6],
 [-8, 4, 8, 6, -7, 23, 13, 19, 6, 10],
 [10, 12, -12, -2, 12, -11, 2, 6, 16, 1],
 [-3, 6, 19, 22, -14, 10, -6, 10, 1, 14]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the determinant of the matrix:
[[-28, 5, -17, -29, -27, 26, 30, 6, -8, -20],
 [4, 3, -10, 30, 28, 23, 4, 11, -22, -17],
 [-1, -29, -14, 30, -16, -20, 18, -2, -20, 23],
 [26, -11, -28, -24, -30, -18, 20, 10, 16, 28],
 [29, -12, -1, -15, -13, 0, 4, -3, 22, 27],
 [10, 25, -6, -19, 17, 13, -7, 1, -8, -5],
 [10, -26, -18, -29, 26, 21, -4, 26, 17, -7],
 [-27, 23, -11, -22, 8, -6, 27, 30, 19, 28],
 [11, 6, -28, 26, 30, -10, -22, 12, 12, -8],
 [-9, -14, -18, -22, -11, -8, -12, 19, -13, 23]]? Round to the nearest integer, then express your answer modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:
[[4, 12, -6, 10, 7, 3, 29, 6, 13, -13],
 [0, 9, 26, 6, -19, -23, -8, 1, -9, 24],
 [0, 0, 14, 2, 21, -28, -20, -19, 10, -5],
 [0, 0, 0, -18, -16, 11, 18, -8, 11, 11],
 [0, 0, 0, 0, 7, -6, -8, 16, -9, -16],
 [0, 0, 0, 0, 0, -28, -17, -20, -29, 12],
 [0, 0, 0, 0, 0, 0, 29, 23, -8, -22],
 [0, 0, 0, 0, 0, 0, 0, 18, 5, 20],
 [0, 0, 0, 0, 0, 0, 0, 0, 2, -1],
 [0, 0, 0, 0, 0, 0, 0, 0, 0, 23]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the value of det(A) where A =
[[-30, 14, -12, 3, 12, -28, -2, 27, -1, -21],
 [-29, 18, -20, -26, 0, 5, 18, 30, 30, -28],
 [-5, -3, -26, 8, 0, -1, 18, -22, -24, 4],
 [27, -10, -26, -8, 0, 3, -11, -10, 20, -15],
 [-6, -24, -23, 0, 27, -29, -9, -29, 22, 0],
 [-16, -25, -27, -8, -7, 15, 8, 1, -3, 27],
 [-6, 22, 22, 15, 20, 8, -17, 25, 11, 4],
 [-18, 23, -10, 11, 6, 24, -20, -27, 17, -27],
 [-22, 7, 27, -26, -18, -20, -24, -17, -16, 2],
 [8, 25, 26, 12, 3, 16, -12, -18, -2, -27]]
Round to the nearest integer, then give your answer as det(A) mod 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:
[[2, -27, -29, 11, 8, -30, 8, 26, 16, -17],
 [26, 3, 11, 13, 21, -27, 21, -27, -8, -7],
 [25, 29, 16, -7, -5, 20, 5, -29, -24, -13],
 [17, -7, -3, 3, 30, 26, -21, -1, 21, -10],
 [24, -4, -26, 4, -7, -5, -30, 1, -21, 27],
 [26, -7, -15, -7, 11, -2, -10, -5, 14, -26],
 [-27, 18, -2, -23, -23, -20, 5, 20, -18, 12],
 [25, 17, 27, 27, 8, -6, -12, 5, 15, -6],
 [17, 2, -11, -18, -3, 1, 14, 28, 15, 18],
 [-2, 30, -21, -11, 1, -3, 28, -19, 7, 23]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:
[[8, 30, -4, 10, -29, -21, -8, 10, -10, -22],
 [-4, -7, -24, 27, -21, 30, 17, 25, -29, 15],
 [-1, 10, 5, 15, -17, 2, -27, 21, 21, 23],
 [2, 20, 27, -7, 26, 25, -17, -19, 18, 1],
 [1, -18, -25, 6, 8, 10, -27, -21, 11, 30],
 [-7, -19, 1, 16, 2, -17, 7, 8, 14, -21],
 [-22, -29, 9, 5, -17, 6, -7, -24, -12, -3],
 [6, -20, 5, -1, 29, 18, 1, 1, 27, -14],
 [-22, -26, -5, -12, 14, 13, -14, -13, -29, -15],
 [22, 6, -30, 1, -16, 3, -11, 15, 23, -18]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the determinant of the matrix:
[[-2, -8, 4, 1, -4, 5, 8, 6, -2, -24],
 [-8, 11, 16, 22, 8, 10, -2, 16, 12, 0],
 [4, 16, 5, -8, 5, -22, 14, -10, 8, -4],
 [1, 22, -8, -7, -3, 28, -22, 18, -20, 2],
 [-4, 8, 5, -3, 12, -28, 2, 5, -10, -4],
 [5, 10, -22, 28, -28, -17, 0, -12, -2, 10],
 [8, -2, 14, -22, 2, 0, -2, -6, 8, 16],
 [6, 16, -10, 18, 5, -12, -6, -9, 10, 26],
 [-2, 12, 8, -20, -10, -2, 8, 10, 22, -12],
 [-24, 0, -4, 2, -4, 10, 16, 26, -12, 28]]? Round to the nearest integer, then express your answer modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:
[[7, -2, 20, 18, -22, 11, -4, -10, 10, 16],
 [-2, 30, -14, -12, 0, -14, 12, 2, -8, 0],
 [20, -14, -5, -16, 8, -19, -2, -8, 14, -12],
 [18, -12, -16, -9, 4, 10, -18, 2, 10, 9],
 [-22, 0, 8, 4, -5, 4, 18, 10, 4, -10],
 [11, -14, -19, 10, 4, -26, 8, 7, -19, -12],
 [-4, 12, -2, -18, 18, 8, 14, -14, -28, 15],
 [-10, 2, -8, 2, 10, 7, -14, 11, -1, -16],
 [10, -8, 14, 10, 4, -19, -28, -1, 4, -20],
 [16, 0, -12, 9, -10, -12, 15, -16, -20, -21]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:
[[-29, 22, 0, 6, 28, 5, 1, 14, 15, 10],
 [22, 10, 12, 1, 26, 12, -23, 0, 12, 8],
 [0, 12, 12, -4, 10, 18, -26, -8, 7, -4],
 [6, 1, -4, 21, -18, -4, 0, 10, 2, -15],
 [28, 26, 10, -18, -20, 4, -28, 4, 10, 6],
 [5, 12, 18, -4, 4, 15, -7, -10, -23, -6],
 [1, -23, -26, 0, -28, -7, -17, -2, 4, 16],
 [14, 0, -8, 10, 4, -10, -2, 20, -2, 0],
 [15, 12, 7, 2, 10, -23, 4, -2, 21, -8],
 [10, 8, -4, -15, 6, -6, 16, 0, -8, -23]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the determinant of the matrix:
[[-12, 3, 24, -2, 28, -28, 26, 6, 13, -6],
 [14, 27, 9, 29, -22, -23, 12, -24, 15, -18],
 [16, 20, 2, 26, 10, 1, -10, -10, 20, 1],
 [-15, 17, 17, 26, -26, 5, -8, -10, 24, -7],
 [-25, -27, -21, -19, 11, -1, -30, -12, 18, 6],
 [-9, -29, -29, 8, 11, -12, 8, -24, 0, -13],
 [-30, -30, -13, 7, -28, -13, -9, -23, 30, 7],
 [-21, -28, 13, -14, -24, 6, -9, 16, 10, -20],
 [17, -12, -2, -3, -3, 30, 5, -7, 13, 24],
 [-20, 0, 26, -23, 17, -13, 1, 9, 0, 29]]? Round to the nearest integer, then express your answer modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the determinant of the matrix:
[[9, -5, -17, 17, -17, -19, -2, -5, 23, -2],
 [1, 28, 5, 16, 21, 24, -5, -23, 23, 27],
 [19, -17, 21, 28, 14, -18, 27, 1, 5, -27],
 [7, -20, -19, -30, 17, 13, -22, 18, 6, 17],
 [-5, -8, -30, -27, -17, -20, 15, 1, 8, 16],
 [13, 23, 23, 14, -10, 8, -28, 6, 0, -7],
 [-14, 11, 2, -1, -20, -29, 0, 27, -27, -24],
 [-20, 14, -4, -4, 15, -3, 9, 17, 28, -24],
 [-30, 0, -22, 28, -11, 28, 7, -16, -28, 10],
 [5, -15, -29, -17, 16, 16, 1, 3, -9, -17]]? Round to the nearest integer, then express your answer modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the determinant of the matrix:
[[-23, -16, 9, 12, -6, 4, 18, -4, 5, 0],
 [-16, -4, -8, -12, 0, -19, 10, -2, 14, 12],
 [9, -8, 26, -10, -13, 10, 0, -8, 26, -23],
 [12, -12, -10, 24, -5, 0, -12, 2, 16, -3],
 [-6, 0, -13, -5, -15, -5, 11, 17, 26, 6],
 [4, -19, 10, 0, -5, -30, 4, 6, -20, 18],
 [18, 10, 0, -12, 11, 4, -9, 0, 3, 20],
 [-4, -2, -8, 2, 17, 6, 0, 23, -20, 8],
 [5, 14, 26, 16, 26, -20, 3, -20, -5, 2],
 [0, 12, -23, -3, 6, 18, 20, 8, 2, -3]]? Round to the nearest integer, then express your answer modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the determinant of the matrix:
[[12, 2, 2, -4, 10, 10, -4, 8, -22, 0],
 [2, -8, -14, 17, 18, -12, 0, -20, 16, -8],
 [2, -14, -27, -2, 12, -16, -4, 23, 6, -6],
 [-4, 17, -2, 18, -5, -10, -12, 2, 13, -4],
 [10, 18, 12, -5, -5, -1, -13, -2, 17, 1],
 [10, -12, -16, -10, -1, -21, 1, 0, -8, 5],
 [-4, 0, -4, -12, -13, 1, 24, -6, 10, -13],
 [8, -20, 23, 2, -2, 0, -6, -25, -10, 4],
 [-22, 16, 6, 13, 17, -8, 10, -10, -9, -25],
 [0, -8, -6, -4, 1, 5, -13, 4, -25, 29]]? Round to the nearest integer, then express your answer modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the value of det(A) where A =
[[-7, 21, 28, -22, -26, 2, 18, 2, 10, 17],
 [0, 14, -10, 29, -26, -24, 10, 29, -3, -23],
 [0, 0, -27, -7, 5, 30, -23, 3, 2, -8],
 [0, 0, 0, 5, 10, -11, -17, -14, -24, -14],
 [0, 0, 0, 0, 29, -2, 10, -12, 2, -15],
 [0, 0, 0, 0, 0, 12, -3, -29, 3, 21],
 [0, 0, 0, 0, 0, 0, 14, 22, -14, -14],
 [0, 0, 0, 0, 0, 0, 0, 25, 13, 24],
 [0, 0, 0, 0, 0, 0, 0, 0, 3, 22],
 [0, 0, 0, 0, 0, 0, 0, 0, 0, 22]]
Round to the nearest integer, then give your answer as det(A) mod 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the determinant of the matrix:
[[-19, 10, -6, 24, 9, 19, 14, -4, -22, 1],
 [0, 13, 12, -24, -18, -15, 30, -3, -5, 27],
 [0, 0, -9, 8, -12, 9, 9, -18, 29, 17],
 [0, 0, 0, -25, 20, -9, 25, -4, -21, -30],
 [0, 0, 0, 0, -27, -12, 22, -3, 26, 1],
 [0, 0, 0, 0, 0, -8, -8, -15, -5, 25],
 [0, 0, 0, 0, 0, 0, -21, -9, -2, -9],
 [0, 0, 0, 0, 0, 0, 0, -14, 30, -29],
 [0, 0, 0, 0, 0, 0, 0, 0, -24, 10],
 [0, 0, 0, 0, 0, 0, 0, 0, 0, 27]]? Round to the nearest integer, then express your answer modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:
[[-25, 28, 28, 18, -16, -25, 14, -9, -27, -16],
 [0, -2, -8, 23, -29, -26, 23, 19, 11, -27],
 [17, -26, 1, 16, -15, 5, -27, 28, -22, 29],
 [-2, -29, -3, -17, 23, 27, -30, 7, 24, 6],
 [10, 8, 23, -11, 15, 14, 27, -14, -15, 12],
 [-28, -21, 15, -26, 21, -14, -22, 11, 23, -22],
 [-9, 7, -11, 16, 22, -21, 12, -20, -18, -3],
 [13, -25, -14, -23, -4, -16, -13, -13, 1, 18],
 [-12, -23, 1, 0, 20, -29, 7, 25, 28, 15],
 [5, -3, -9, 12, 1, -17, -27, 10, -21, 23]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:
[[-21, -1, 8, 12, -14, 22, -7, -11, -12, -2],
 [-1, -10, -6, -7, 5, 6, 9, 12, -2, 2],
 [8, -6, -20, 0, -17, 6, -2, 6, 11, 0],
 [12, -7, 0, -5, -4, -16, 22, -2, -10, -10],
 [-14, 5, -17, -4, -21, -7, -2, 1, -25, 1],
 [22, 6, 6, -16, -7, -23, -14, -8, 1, -14],
 [-7, 9, -2, 22, -2, -14, -14, 17, 24, 0],
 [-11, 12, 6, -2, 1, -8, 17, -19, -12, -20],
 [-12, -2, 11, -10, -25, 1, 24, -12, 13, 6],
 [-2, 2, 0, -10, 1, -14, 0, -20, 6, 2]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the value of det(A) where A =
[[5, 19, -6, 17, -5, 18, -29, 6, -1, 9],
 [-12, -8, 3, -4, 7, 15, 8, 25, -16, 23],
 [16, -22, -13, -6, -13, 25, -12, -13, -29, -19],
 [14, 27, 21, -2, 20, 13, -27, 11, -20, -18],
 [4, 12, -23, -16, -6, -4, 15, 23, 25, 9],
 [-15, -2, 24, 16, -16, 11, 6, -26, 30, 8],
 [10, -12, 23, -18, 23, -3, 17, 20, 29, 22],
 [-9, 3, -14, -30, 5, 8, 18, 24, 14, -9],
 [-24, 5, 24, -26, 6, -11, -15, -29, -11, 30],
 [24, 14, 19, 13, -28, -25, 3, -4, -11, 11]]
Round to the nearest integer, then give your answer as det(A) mod 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the value of det(A) where A =
[[-20, 9, -1, -7, 22, -5, -29, 3, 22, -15],
 [0, -29, 27, -19, -24, 20, 28, -17, 1, -24],
 [0, 0, 23, 20, 4, -13, 1, -18, -21, 16],
 [0, 0, 0, -9, -11, -22, -21, 13, 29, 25],
 [0, 0, 0, 0, 21, 13, 17, -24, 26, -28],
 [0, 0, 0, 0, 0, 20, -24, 20, 15, -16],
 [0, 0, 0, 0, 0, 0, -17, -13, -23, 2],
 [0, 0, 0, 0, 0, 0, 0, 5, -12, -13],
 [0, 0, 0, 0, 0, 0, 0, 0, 22, -27],
 [0, 0, 0, 0, 0, 0, 0, 0, 0, 23]]
Round to the nearest integer, then give your answer as det(A) mod 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute |A| for the matrix A =
[[9, -22, -16, 6, 13, 13, 13, -22, 1, 27],
 [-14, 29, -28, 16, 22, 16, -19, 7, 28, 2],
 [2, -4, -16, -27, -1, -14, 10, -28, 27, 3],
 [-2, 13, 26, -15, -6, -20, -6, -18, -28, 27],
 [-11, -10, 16, 18, 13, -16, -23, 15, 28, 8],
 [24, 22, -1, -13, -23, -21, 9, 23, 16, 25],
 [28, -12, -22, -22, 20, -3, -12, 0, 17, 12],
 [-5, -3, 0, 27, -19, 7, -16, -28, -2, 23],
 [-23, -29, 23, -28, -1, 2, 5, -10, 4, -15],
 [-21, 13, -30, -30, 1, 9, -14, -25, -26, 10]]
Round to the nearest integer, then take the result modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:
[[-4, 3, -30, 7, 24, 1, 2, 28, 25, 10],
 [24, 26, -12, -16, -21, 11, -5, -12, 6, -29],
 [-23, 10, -20, 25, 11, 22, -26, -20, -15, 26],
 [4, -4, -20, 5, -1, 19, -28, 7, 21, -7],
 [-26, -18, 12, -9, 3, -8, 13, -17, -15, 8],
 [11, -15, -25, -22, 20, -3, -29, 30, 12, 19],
 [-12, 28, 9, -4, -16, -19, 10, 25, -10, 22],
 [23, 19, -30, -14, 14, -18, -4, 2, -28, 3],
 [18, 22, -20, -10, -12, 23, -8, 19, -20, 26],
 [17, 19, -12, -17, -24, 1, 17, -21, -1, 13]]

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[User]
What is the determinant of the matrix:
[[24, 21, -2, 23, -23, -23, -2, 5, -12, 4],
 [0, -18, 30, 11, 14, -27, 1, -20, -1, 8],
 [0, 0, -24, 23, -17, -30, -13, -30, 26, -25],
 [0, 0, 0, -21, -21, 10, -3, -5, -7, 15],
 [0, 0, 0, 0, 28, -8, 10, -12, -18, -17],
 [0, 0, 0, 0, 0, 13, 9, 4, 9, 17],
 [0, 0, 0, 0, 0, 0, -21, -23, -15, -21],
 [0, 0, 0, 0, 0, 0, 0, -15, -22, 29],
 [0, 0, 0, 0, 0, 0, 0, 0, 28, 8],
 [0, 0, 0, 0, 0, 0, 0, 0, 0, 27]]? Round to the nearest integer, then express your answer modulo 1000.

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[User]
Determine the value of det(A) where A =
[[-10, 14, 17, 21, 27, -4, 8, -3, 29, -3],
 [0, 15, -22, 29, -30, -9, 24, 24, -8, 30],
 [0, 0, 7, -1, -22, -18, 26, 3, 25, -30],
 [0, 0, 0, -24, -23, -15, -8, 28, -1, -22],
 [0, 0, 0, 0, -3, 20, 2, -5, 2, -18],
 [0, 0, 0, 0, 0, -26, 30, 28, -5, -24],
 [0, 0, 0, 0, 0, 0, 17, 0, 27, -9],
 [0, 0, 0, 0, 0, 0, 0, 18, -29, 27],
 [0, 0, 0, 0, 0, 0, 0, 0, -22, 16],
 [0, 0, 0, 0, 0, 0, 0, 0, 0, 3]]
Round to the nearest integer, then give your answer as det(A) mod 1000.

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[User]
Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:
[[-3, 17, -8, 12, -17, -10, 22, -29, 29, -6],
 [25, 13, -30, -30, -11, -17, 11, 25, -30, 19],
 [17, 3, 22, 11, -20, -10, 16, 29, -18, -6],
 [-4, -8, 26, -19, -1, -19, -25, -6, -6, -1],
 [8, -16, -19, -20, 14, 24, -11, 0, -26, -25],
 [4, 13, -10, 15, -24, -15, -29, -24, 30, 24],
 [5, 21, 25, 18, -3, -19, 23, 1, -26, -13],
 [-17, 19, -25, -7, -2, 7, -30, -28, 2, -3],
 [29, 5, 12, 21, 17, -5, -4, -11, -10, -28],
 [-17, -21, 8, 28, -14, -5, 30, 30, 28, -22]]

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[User]
Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:
[[10, 0, 29, 0, -7, 10, -6, -8, -19, 20],
 [0, -15, -12, -13, -27, -30, -8, -30, 28, -10],
 [0, 0, -9, 26, -15, -13, 21, -5, -4, 30],
 [0, 0, 0, -7, 14, 8, 10, -6, 11, 25],
 [0, 0, 0, 0, -5, -13, -20, 5, 26, -14],
 [0, 0, 0, 0, 0, 12, 19, -12, 24, 20],
 [0, 0, 0, 0, 0, 0, 28, -2, 8, -27],
 [0, 0, 0, 0, 0, 0, 0, -18, -28, -22],
 [0, 0, 0, 0, 0, 0, 0, 0, 1, -14],
 [0, 0, 0, 0, 0, 0, 0, 0, 0, -12]]

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[User]
Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:
[[-8, -6, 26, 4, 4, 28, 7, -1, -19, 13],
 [2, -18, -10, -11, 29, -2, 11, -2, -14, -7],
 [28, 4, 28, 26, 2, -22, -10, -25, 13, 5],
 [-1, -13, -21, 25, -14, -7, 4, -11, -17, 27],
 [-27, 14, 29, 29, -16, 4, 30, 11, 20, -2],
 [-26, 17, -8, -12, -28, -9, -16, 25, -23, -15],
 [18, 13, 7, -1, -28, -6, -16, -14, -23, -19],
 [-5, 27, -17, -24, 21, 25, -6, -1, -13, -21],
 [-1, 9, 30, -10, -29, 4, -3, -14, 3, 27],
 [-27, 2, 10, 18, 11, -7, 0, -22, 3, 10]]

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[User]
Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:
[[22, -29, -2, 2, -9, 3, 21, 13, -19, -21],
 [0, 22, -9, -17, 3, 28, 28, 22, 28, -17],
 [0, 0, 9, 18, 8, -16, -14, -5, 20, 11],
 [0, 0, 0, -20, 2, 25, 5, -23, 21, 27],
 [0, 0, 0, 0, 13, -30, -19, -15, -29, -10],
 [0, 0, 0, 0, 0, -4, -8, 30, -29, 4],
 [0, 0, 0, 0, 0, 0, 1, 27, -12, -13],
 [0, 0, 0, 0, 0, 0, 0, -20, -4, -15],
 [0, 0, 0, 0, 0, 0, 0, 0, 9, 8],
 [0, 0, 0, 0, 0, 0, 0, 0, 0, -24]]

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[User]
Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:
[[29, -16, 25, -11, -26, -10, -14, -1, 3, -27],
 [0, -26, 7, -21, -20, 5, -13, 4, -15, -7],
 [0, 0, -24, -22, -9, -16, 19, -14, -17, -2],
 [0, 0, 0, -9, -4, 19, 5, 24, -25, -1],
 [0, 0, 0, 0, -20, -8, 13, -25, 29, 18],
 [0, 0, 0, 0, 0, 3, 4, 10, 1, 5],
 [0, 0, 0, 0, 0, 0, 4, -19, -26, 1],
 [0, 0, 0, 0, 0, 0, 0, -20, -2, -27],
 [0, 0, 0, 0, 0, 0, 0, 0, 18, 10],
 [0, 0, 0, 0, 0, 0, 0, 0, 0, 28]]

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[User]
Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:
[[-4, 14, 14, 12, 14, 0, -2, 9, 2, -21],
 [14, 22, 20, 22, 21, -6, 0, 12, 2, -8],
 [14, 20, -10, 10, -4, 10, 10, 18, -12, -24],
 [12, 22, 10, -26, -2, 10, -10, -1, 16, -23],
 [14, 21, -4, -2, 10, -24, -24, -22, 10, -1],
 [0, -6, 10, 10, -24, 15, 24, -3, 10, 2],
 [-2, 0, 10, -10, -24, 24, 28, -20, -8, -4],
 [9, 12, 18, -1, -22, -3, -20, 12, -16, 28],
 [2, 2, -12, 16, 10, 10, -8, -16, -1, 5],
 [-21, -8, -24, -23, -1, 2, -4, 28, 5, 2]]

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[User]
Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:
[[-13, -30, 13, 16, 27, 14, 29, 7, 0, -12],
 [0, -5, -26, 1, -14, 29, -19, -23, -10, -15],
 [0, 0, 30, -20, 25, -17, -24, 1, -19, 13],
 [0, 0, 0, 30, 3, -28, 27, 16, 8, 14],
 [0, 0, 0, 0, 20, -5, -14, -5, -27, 26],
 [0, 0, 0, 0, 0, -6, -23, -24, -3, -11],
 [0, 0, 0, 0, 0, 0, 11, 21, -22, -19],
 [0, 0, 0, 0, 0, 0, 0, 22, 21, 22],
 [0, 0, 0, 0, 0, 0, 0, 0, 13, -21],
 [0, 0, 0, 0, 0, 0, 0, 0, 0, 6]]

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[User]
Determine the value of det(A) where A =
[[20, -7, -24, 24, -11, -10, 1, -2, -17, 21],
 [0, -25, 1, -13, 30, 6, -20, 10, -27, -7],
 [0, 0, 9, 23, -18, 24, -25, -14, -4, -5],
 [0, 0, 0, 4, 25, -7, 3, -3, 4, -27],
 [0, 0, 0, 0, 1, -18, 15, -22, -10, -17],
 [0, 0, 0, 0, 0, -2, -9, 24, -5, -20],
 [0, 0, 0, 0, 0, 0, 2, -12, -4, 13],
 [0, 0, 0, 0, 0, 0, 0, -12, -15, 13],
 [0, 0, 0, 0, 0, 0, 0, 0, 30, 21],
 [0, 0, 0, 0, 0, 0, 0, 0, 0, 17]]
Round to the nearest integer, then give your answer as det(A) mod 1000.

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[User]
Determine the value of det(A) where A =
[[15, -2, 29, -11, 28, -15, -20, -1, 18, -28],
 [13, -7, 2, -5, 24, 7, -4, 6, 14, 22],
 [-25, 12, -27, 4, 11, -13, 11, 20, -4, 27],
 [21, -6, -20, 11, -15, 7, 10, 24, 28, 22],
 [1, 17, -22, 24, 22, -7, -5, -30, -1, -25],
 [-22, -21, -11, 11, -19, -22, 4, 23, 13, -14],
 [14, 13, -30, -23, -8, 2, 25, 2, 6, 4],
 [-17, -18, -3, 26, -30, 22, 8, 2, -20, -13],
 [4, -30, 25, 17, -16, -4, 9, -30, 0, 27],
 [8, 23, 0, -22, 14, 20, 11, -11, 2, -29]]
Round to the nearest integer, then give your answer as det(A) mod 1000.

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[User]
What is the determinant of the matrix:
[[13, 12, -23, -23, 27, 9, -29, 2, 17, -5],
 [5, 6, 4, 10, 0, 21, 22, 21, 24, 15],
 [1, 24, 4, 16, 29, -22, 18, 11, 4, 9],
 [-28, -8, 15, -26, -15, -27, 7, 3, -13, -6],
 [14, 29, 19, 12, -23, -16, 1, -15, 22, -22],
 [-7, 1, 24, -15, 3, -21, -8, -15, 16, 13],
 [-27, 16, -7, 30, -28, -17, 15, -3, 28, 10],
 [-29, 9, -28, -1, -26, -16, -28, 19, -5, 15],
 [-8, -16, 30, -15, -22, 26, 17, -25, -20, -18],
 [-26, 10, -7, 2, 27, -17, 14, 14, -30, -2]]? Round to the nearest integer, then express your answer modulo 1000.

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