[User]
What is the determinant of the matrix:
[[7, 6, -3, 11, 5, 3],
 [0, 13, -6, -3, -6, 14],
 [0, 0, 10, -8, -3, -10],
 [0, 0, 0, 12, -2, 2],
 [0, 0, 0, 0, 12, -9],
 [0, 0, 0, 0, 0, 2]]? Round to the nearest integer, then express your answer modulo 1000.

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

dataset: MATH


[User]
What is the determinant of the matrix:
[[0, -9, 5, 9, -3, -1],
 [8, -13, 3, 10, -4, -4],
 [-5, 6, 3, 7, 3, 1],
 [-9, -8, 5, -13, -10, 4],
 [0, 5, -8, 4, 2, -8],
 [-12, -15, -3, -4, -8, -8]]? 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:
[[-3, -3, 5, 4, 5, -15],
 [0, 2, -8, -4, 10, -7],
 [0, 0, 14, 0, 6, 5],
 [0, 0, 0, -12, 8, -10],
 [0, 0, 0, 0, -11, 6],
 [0, 0, 0, 0, 0, 11]]

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


[User]
What is the determinant of the matrix:
[[8, 3, 9, 7, -12, 14],
 [-2, 3, -4, 2, 6, -13],
 [-15, 2, 3, -11, 13, 12],
 [-12, 7, -11, 10, -9, -11],
 [-8, -13, -10, 10, 3, 3],
 [5, -7, 9, 12, 6, -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:
[[13, 0, -8, -4, 10, -3],
 [0, 3, 2, 5, 10, -4],
 [-8, 2, -7, -4, 10, 0],
 [-4, 5, -4, -3, -10, -6],
 [10, 10, 10, -10, -11, -2],
 [-3, -4, 0, -6, -2, -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, 6, -4, 0, -1, -6],
 [6, 13, -8, -11, 5, -1],
 [-4, -8, -14, 0, 6, 10],
 [0, -11, 0, 12, -6, 10],
 [-1, 5, 6, -6, -1, -2],
 [-6, -1, 10, 10, -2, -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:
[[-1, 10, -1, -1, -15, -4],
 [-4, 7, -9, -1, -12, -7],
 [-6, 2, -8, 11, -7, -11],
 [1, -1, 4, -6, -15, -10],
 [-1, 2, -8, 0, 15, -13],
 [0, 7, 2, 11, 12, -11]]

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, -6, -7, 0, -6, 8],
 [-6, -9, 2, -12, 6, -2],
 [-7, 2, 8, -10, 3, 2],
 [0, -12, -10, -3, 0, 4],
 [-6, 6, 3, 0, 4, 2],
 [8, -2, 2, 4, 2, -5]]

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


[User]
What is the determinant of the matrix:
[[-2, 1, 1, 5, -7, 0],
 [1, 0, 8, -2, -5, -5],
 [1, 8, 5, -2, 2, -10],
 [5, -2, -2, -9, 4, 0],
 [-7, -5, 2, 4, -13, 3],
 [0, -5, -10, 0, 3, -2]]? 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:
[[-2, 8, -4, 4, 8, 5],
 [8, -2, -8, -8, -2, -1],
 [-4, -8, 10, 2, -6, 2],
 [4, -8, 2, 5, 2, -9],
 [8, -2, -6, 2, 11, 1],
 [5, -1, 2, -9, 1, -5]]

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


[User]
Compute |A| for the matrix A =
[[7, 2, 5, 4, 5, 4],
 [2, 0, -7, 2, -1, 6],
 [5, -7, 0, 0, 8, 12],
 [4, 2, 0, 1, 4, 2],
 [5, -1, 8, 4, 13, 2],
 [4, 6, 12, 2, 2, 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:
[[-11, 6, -12, 8, -10, 0],
 [-5, -8, -7, 13, 1, -14],
 [10, 3, 9, -9, 14, 11],
 [8, -6, 4, 0, 11, -4],
 [15, 0, -11, -10, -2, -11],
 [-9, 0, 4, 9, 14, 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:
[[1, 2, 10, 2, 0, 6],
 [2, 10, 0, 3, -6, -6],
 [10, 0, -3, 6, 4, -8],
 [2, 3, 6, 2, 2, 8],
 [0, -6, 4, 2, 3, 0],
 [6, -6, -8, 8, 0, 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:
[[-7, 3, -8, 0, -15, 1],
 [0, -6, 14, 13, -5, -5],
 [0, 0, 9, -14, -13, 4],
 [0, 0, 0, 3, -13, -12],
 [0, 0, 0, 0, 6, 14],
 [0, 0, 0, 0, 0, -7]]

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, -3, -12, 14, 8, -13],
 [-10, 3, -3, -2, 4, 9],
 [-10, 13, -6, -10, -15, -15],
 [4, 9, -5, 4, 12, -8],
 [-5, 15, -4, -4, 0, 12],
 [10, -3, 2, -3, 9, -5]]

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:
[[-2, 0, 8, 3, 0, -6],
 [0, 10, 6, 9, -14, 4],
 [8, 6, 8, -4, 12, 0],
 [3, 9, -4, 0, 1, -1],
 [0, -14, 12, 1, 15, -14],
 [-6, 4, 0, -1, -14, 8]]

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


[User]
Determine the value of det(A) where A =
[[12, 7, -3, 3, 15, 5],
 [4, -12, -3, -12, -5, 10],
 [12, -14, -13, -7, 5, 14],
 [4, 7, 11, 7, -7, 5],
 [3, 6, 1, -11, -5, -6],
 [-9, 15, 2, 6, 9, 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]
Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:
[[13, -12, 5, 3, 7, 4],
 [0, 6, -12, -3, -10, 10],
 [0, 0, 14, 10, 4, 15],
 [0, 0, 0, 7, -14, -13],
 [0, 0, 0, 0, -8, -3],
 [0, 0, 0, 0, 0, -1]]

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


[User]
Determine the value of det(A) where A =
[[11, 1, -4, 0, 12, 13],
 [0, -5, -9, -5, -5, -11],
 [0, 0, 2, -4, 11, -2],
 [0, 0, 0, -8, -15, -1],
 [0, 0, 0, 0, 11, 5],
 [0, 0, 0, 0, 0, -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]
Determine the value of det(A) where A =
[[5, -2, 14, 15, 8, 6],
 [2, 10, -2, 3, -1, -3],
 [-8, 1, 2, 0, -15, -10],
 [9, -11, -5, 0, 5, -3],
 [11, -8, 9, 9, 6, -7],
 [-13, 11, -13, -7, -7, -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:
[[14, 4, 10, 12, -8, -12],
 [0, -13, -9, 6, 6, -15],
 [0, 0, 2, -10, -10, -15],
 [0, 0, 0, -8, 15, -13],
 [0, 0, 0, 0, -3, -1],
 [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:
[[-9, -5, -12, 1, -14, -3],
 [0, 13, 3, 8, 2, -15],
 [0, 0, 13, -15, 7, 5],
 [0, 0, 0, -8, -6, -13],
 [0, 0, 0, 0, 2, -3],
 [0, 0, 0, 0, 0, 6]]

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, 4, 4, 2, 5, -4],
 [4, 6, 0, 0, 11, 2],
 [4, 0, 7, 1, 4, -5],
 [2, 0, 1, 8, 10, 3],
 [5, 11, 4, 10, 1, -4],
 [-4, 2, -5, 3, -4, 0]]

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, 3, 5, -15, -6, 4],
 [0, 3, -12, 7, -3, 8],
 [0, 0, -12, 5, -8, -3],
 [0, 0, 0, 7, 12, 14],
 [0, 0, 0, 0, 15, -3],
 [0, 0, 0, 0, 0, 3]]

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:
[[5, -10, -14, 8, -13, -14],
 [0, 14, 1, 11, 14, -7],
 [0, 0, -1, -6, 5, -13],
 [0, 0, 0, 5, 3, -14],
 [0, 0, 0, 0, -12, -4],
 [0, 0, 0, 0, 0, 9]]

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


[User]
Determine the value of det(A) where A =
[[14, 8, 9, -5, 10, -11],
 [0, -15, 8, 10, 4, -8],
 [0, 0, -8, 13, -7, 15],
 [0, 0, 0, 1, 10, -3],
 [0, 0, 0, 0, 15, -14],
 [0, 0, 0, 0, 0, -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]
What is the determinant of the matrix:
[[5, 2, -2, -3, -5, 6],
 [2, 14, 4, 10, -2, 6],
 [-2, 4, 4, -2, 4, 0],
 [-3, 10, -2, -4, 0, -7],
 [-5, -2, 4, 0, 9, 2],
 [6, 6, 0, -7, 2, 0]]? 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:
[[1, -4, 12, -6, 5, -12],
 [-4, -10, 3, -2, -5, 2],
 [12, 3, 11, -8, 2, 0],
 [-6, -2, -8, 4, 0, 2],
 [5, -5, 2, 0, 3, 6],
 [-12, 2, 0, 2, 6, -7]]

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


[User]
What is the determinant of the matrix:
[[-7, -1, 2, 0, -10, -2],
 [-1, -13, 7, -8, -6, 2],
 [2, 7, -3, 8, -12, -1],
 [0, -8, 8, -9, 10, 6],
 [-10, -6, -12, 10, -1, 5],
 [-2, 2, -1, 6, 5, -5]]? 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:
[[2, 0, -3, -11, 14, -2],
 [0, 15, -14, 7, -11, 14],
 [0, 0, 6, 0, -10, 14],
 [0, 0, 0, -10, -13, 14],
 [0, 0, 0, 0, 11, -12],
 [0, 0, 0, 0, 0, -1]]? 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:
[[2, -10, 14, -7, 3, 10],
 [0, -8, -9, -7, -14, -5],
 [0, 0, -11, 0, -15, 7],
 [0, 0, 0, 2, -6, 11],
 [0, 0, 0, 0, 5, -6],
 [0, 0, 0, 0, 0, 11]]

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, -1, 0, 4, -1, -6],
 [-1, 5, -4, 0, -4, 0],
 [0, -4, 1, -6, -2, -7],
 [4, 0, -6, -4, -4, -4],
 [-1, -4, -2, -4, -1, -9],
 [-6, 0, -7, -4, -9, -4]]

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, -4, -2, -12, -7, -10],
 [-4, 9, 6, 6, -3, 10],
 [-2, 6, 4, 2, -9, 8],
 [-12, 6, 2, -15, -2, -2],
 [-7, -3, -9, -2, -13, -4],
 [-10, 10, 8, -2, -4, 4]]

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, 0, 7, -15, 7, 7],
 [13, -6, 8, 10, -6, 14],
 [-12, -11, -6, -1, -4, -13],
 [-4, -13, -2, -6, 1, 13],
 [13, -12, 13, -14, 7, 4],
 [8, 0, -7, -6, -2, 9]]

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


[User]
What is the determinant of the matrix:
[[6, -12, 2, 15, 3, -13],
 [-14, 3, 5, -15, 15, -10],
 [-8, 9, -8, 5, -9, -8],
 [-2, 1, 5, 4, 2, -9],
 [10, -3, -1, 10, -15, -3],
 [8, 0, 5, 7, -7, -10]]? 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:
[[-2, -9, 1, 1, 14, 7],
 [-9, -8, 0, 0, -4, 8],
 [1, 0, 0, -4, -6, 0],
 [1, 0, -4, 0, 6, -4],
 [14, -4, -6, 6, -4, -4],
 [7, 8, 0, -4, -4, -9]]

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


[User]
Compute |A| for the matrix A =
[[-13, 1, 7, 3, -3, -12],
 [-12, -13, 1, 11, 10, 0],
 [6, 14, 8, -9, -13, -11],
 [-2, 10, 8, -10, -2, -6],
 [11, 4, -7, -4, -6, 13],
 [9, -7, -11, 4, -13, 8]]
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 =
[[6, 8, 10, 0, -12, 6],
 [8, 3, 4, -5, -6, -4],
 [10, 4, 5, -14, 10, -6],
 [0, -5, -14, 13, -7, -8],
 [-12, -6, 10, -7, -3, 2],
 [6, -4, -6, -8, 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 =
[[-8, -2, -12, 2, -7, -13],
 [-5, -15, -7, 0, 12, -5],
 [10, 15, 5, -11, -7, 12],
 [-3, -8, -9, 6, 3, 13],
 [12, 13, 4, -6, -7, 0],
 [8, -5, 0, 11, -12, -13]]
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:
[[9, 0, 12, 13, -1, -4],
 [-7, -10, -5, -3, 4, 1],
 [-5, 9, -4, -9, -4, 11],
 [-6, 8, 7, -7, 3, -9],
 [-2, -9, 3, 6, 4, 8],
 [-13, 2, 13, -5, 6, -1]]? 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 =
[[-4, 7, 2, -6, 0, 0],
 [7, 9, 0, 2, 3, -8],
 [2, 0, -8, 12, 8, 4],
 [-6, 2, 12, -6, 6, -8],
 [0, 3, 8, 6, 5, 6],
 [0, -8, 4, -8, 6, 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]
Determine the value of det(A) where A =
[[3, 10, 8, 4, 13, -10],
 [0, 2, -14, -8, -9, -9],
 [0, 0, 3, -15, 14, -15],
 [0, 0, 0, -12, -5, -12],
 [0, 0, 0, 0, 3, -6],
 [0, 0, 0, 0, 0, -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:
[[3, 7, -15, -2, 8, 9],
 [0, 14, -6, 12, -1, 14],
 [0, 0, 15, 9, -6, -4],
 [0, 0, 0, 13, 1, 4],
 [0, 0, 0, 0, 1, 1],
 [0, 0, 0, 0, 0, -3]]

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


[User]
Compute |A| for the matrix A =
[[-4, 1, 9, -15, -8, -5],
 [0, -5, -10, 8, -12, -8],
 [0, 0, -4, -15, 0, 12],
 [0, 0, 0, -10, -1, -12],
 [0, 0, 0, 0, 2, -8],
 [0, 0, 0, 0, 0, -10]]
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:
[[15, 0, 0, -6, 2, 4],
 [0, -2, 12, 4, -8, -4],
 [0, 12, 8, 2, -14, -2],
 [-6, 4, 2, 2, 0, -4],
 [2, -8, -14, 0, -5, 10],
 [4, -4, -2, -4, 10, 0]]? 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:
[[10, 0, -4, -2, 0, 6],
 [0, -1, -3, 0, 0, -1],
 [-4, -3, -9, 3, 0, -10],
 [-2, 0, 3, -11, -10, -8],
 [0, 0, 0, -10, -9, -8],
 [6, -1, -10, -8, -8, 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:
[[15, 1, 5, -3, -9, -11],
 [-11, 4, 4, 13, -4, 1],
 [-7, -4, -14, 1, -9, -3],
 [9, 0, 1, 13, -7, 14],
 [-4, 6, 4, 6, 14, -2],
 [14, -1, 6, 0, -4, 6]]

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


[User]
Determine the value of det(A) where A =
[[-11, 10, 7, -4, 8, -5],
 [10, 8, 2, 2, 2, 0],
 [7, 2, -2, 0, -3, -3],
 [-4, 2, 0, -3, 2, -10],
 [8, 2, -3, 2, 0, 0],
 [-5, 0, -3, -10, 0, 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]
Determine the value of det(A) where A =
[[-1, -7, -10, -14, -14, -5],
 [10, -11, 8, 0, 3, -5],
 [-6, 12, -1, 2, 3, -8],
 [13, -8, 8, 7, 1, -1],
 [14, 15, 11, 8, -4, 15],
 [14, -11, 7, 9, 1, 1]]
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:
[[-11, -4, -10, -6, 2, -6],
 [0, 4, 2, 6, -6, -8],
 [0, 0, -12, -5, 3, 9],
 [0, 0, 0, 2, 3, 9],
 [0, 0, 0, 0, 6, 0],
 [0, 0, 0, 0, 0, -10]]? Round to the nearest integer, then express your answer modulo 1000.

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