[User]
Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:
[[-10, 3, 9],
 [-9, 6, -10],
 [1, 0, -9]]

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

dataset: MATH


[User]
Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:
[[5, 8, 5],
 [0, 6, 7],
 [0, 0, 5]]

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


[User]
Compute |A| for the matrix A =
[[8, -5, 0],
 [5, 7, 8],
 [-9, -1, 7]]
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, -7, -5],
 [0, -3, -7],
 [0, 0, 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:
[[3, -2, 0],
 [-2, 3, -7],
 [0, -7, -3]]

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


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

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


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

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


[User]
Determine the value of det(A) where A =
[[-1, -8, -3],
 [-8, 2, -6],
 [-3, -6, -3]]
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 =
[[10, -3, -9],
 [0, 1, -3],
 [0, 0, 3]]
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, 7, -2],
 [3, 9, -10],
 [-7, -6, 3]]

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


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

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


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

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


[User]
Compute |A| for the matrix A =
[[9, -9, 6],
 [-9, 3, -2],
 [6, -2, 9]]
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 =
[[-10, 10, -6],
 [0, -3, 9],
 [0, 0, -3]]
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, -2, -8],
 [0, 2, 9],
 [0, 0, 2]]
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 =
[[2, -9, 9],
 [-4, 3, 4],
 [-4, 2, -8]]
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 =
[[8, 9, -8],
 [0, 10, 10],
 [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]
Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:
[[9, 2, 1],
 [-9, -2, -10],
 [-6, 3, -5]]

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


[User]
Compute |A| for the matrix A =
[[-2, 1, -10],
 [0, 4, 9],
 [0, 0, 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:
[[5, -9, -2],
 [0, -6, 7],
 [10, 10, 10]]

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


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

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


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

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


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

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


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

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


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

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


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

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:
[[10, -10, -10, 12],
 [-9, -3, -2, -7],
 [-5, 5, 4, -11],
 [5, 5, 12, -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:
[[7, -8, 7, 1],
 [-7, -9, 10, -6],
 [-1, -9, 5, -8],
 [-12, -10, -12, 3]]

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


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

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


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

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, -2, 4, 4],
 [-2, 6, -4, -1],
 [4, -4, 8, 8],
 [4, -1, 8, -2]]

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:
[[4, -7, -5, 8],
 [-7, -6, 5, -2],
 [-5, 5, 10, 1],
 [8, -2, 1, 9]]

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


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

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, 2],
 [2, -6, 9, -1],
 [-7, -6, 7, -9],
 [-11, 9, -3, -10]]

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


[User]
Compute |A| for the matrix A =
[[7, 4, 10, 9],
 [4, -6, 8, -9],
 [10, 8, 3, 3],
 [9, -9, 3, -6]]
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 =
[[5, 12, -9, 10],
 [0, -4, 2, -7],
 [0, 0, -2, -8],
 [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]
Compute |A| for the matrix A =
[[-11, 11, 3, 5],
 [0, -3, 9, -12],
 [0, 0, 5, -4],
 [0, 0, 0, -3]]
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 =
[[5, 10, -12, -9],
 [-1, -11, 9, 11],
 [0, -12, 10, 4],
 [-8, 12, 7, 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]
Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:
[[8, -7, 1, 5],
 [0, -7, -12, 2],
 [0, 0, -6, 0],
 [0, 0, 0, 5]]

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


[User]
Determine the value of det(A) where A =
[[11, -2, 0, 0],
 [0, -3, 12, -3],
 [0, 0, 5, 2],
 [0, 0, 0, 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 =
[[-9, -4, -10, -6],
 [-4, -5, 0, 4],
 [-10, 0, -12, 4],
 [-6, 4, 4, 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]
What is the determinant of the matrix:
[[-12, 0, 4, 0],
 [0, -2, 0, 0],
 [4, 0, 6, 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}


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

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


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

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


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

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


[User]
Compute |A| for the matrix A =
[[-1, -1, -1, 7],
 [10, -1, -2, -1],
 [-11, -2, -9, -4],
 [-9, -2, -1, -10]]
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 =
[[12, -9, 0, 0],
 [-8, 9, -2, 0],
 [4, -4, 0, 10],
 [4, 6, 9, 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]
Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:
[[7, 7, 6, 0],
 [7, -4, 6, 0],
 [6, 6, -2, 2],
 [0, 0, 2, 0]]

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


[User]
What is the determinant of the matrix:
[[10, -2, -12, 3],
 [0, -3, -10, -5],
 [0, 0, 1, -2],
 [0, 0, 0, 4]]? Round to the nearest integer, then express your answer modulo 1000.

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