messages listlengths 1 1 | ground_truth stringclasses 992
values | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Compute |A| for the matrix A =\n[[7, 9, 6, 8],\n [0, -6, -8, -9],\n [0, 0, 6, 2],\n [0, 0, 0, -5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 260 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-5, 6, 0, -1],\n [6, 7, 7, 2],\n [0, 7, -12, 8],\n [-1, 2, 8, -12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 113 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-4, 10, -7, -1],\n [2, 2, -4, -5],\n [6, 11, -11, 12],\n [8, -12, -2, -6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 872 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[1, 4, 3, -7],\n [0, -4, 4, 9],\n [0, 0, -5, 9],\n [0, 0, 0, -9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 820 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-1, -5, 2, 6],\n [-5, 7, 2, -4],\n [2, 2, 2, 6],\n [6, -4, 6, 8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 880 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, 1, 5, 2],\n [4, -11, 0, -10],\n [10, -2, 1, -11],\n [3, -12, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 831 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, 5, -10, -4],\n [0, -4, 9, 10],\n [0, 0, 8, 10],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 232 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-7, -1, 2, 0],\n [0, -4, 1, -7],\n [0, 0, 12, 6],\n [0, 0, 0, -10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 640 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[3, 2, 10, 5],\n [-11, -4, -3, 3],\n [12, 8, -12, 3],\n [-3, 2, 3, -2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 94 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-4, 11, 6, -1],\n [0, 12, -7, 2],\n [-2, 9, 12, 4],\n [-8, 1, 5, 0]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 466 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, 12, 8, -11],\n [-7, -2, 4, 3],\n [8, 10, -12, 5],\n [-8, -8, 12, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 408 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[12, -9, 1, -6],\n [-6, 9, 4, -3],\n [7, -1, 12, -9],\n [0, 2, -7, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 404 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 12, -8, -3],\n [-12, -9, -9, -11],\n [-4, -6, -10, 3],\n [12, 7, 8, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 945 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[8, 8, -5, -10],\n [0, -3, 2, 4],\n [0, 0, 12, 11],\n [0, 0, 0, 5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 560 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, -4, 12, -4],\n [0, -8, -6, 0],\n [0, 0, 7, -7],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 440 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[10, 2, 11, -12],\n [0, 11, 1, 0],\n [0, 0, -5, 3],\n [0, 0, 0, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 100 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-7, -3, -10, 12],\n [0, 12, 5, 0],\n [0, 0, -2, 12],\n [0, 0, 0, -12]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 984 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, 5, 2, 0],\n [5, 5, 6, 2],\n [2, 6, -2, -8],\n [0, 2, -8, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 36 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-1, -9, -2, 4],\n [11, 9, -5, 8],\n [3, 5, 0, 1],\n [-4, 9, 6, 2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 635 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-10, -3, 3, 9],\n [-11, -12, 1, -1],\n [-9, -12, 6, 0],\n [-12, 2, -5, 12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 201 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-2, 1, 1, 9],\n [0, -8, 7, -4],\n [0, 0, -5, 6],\n [0, 0, 0, -4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 320 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-1, 4, -8, 2],\n [4, 3, -2, -4],\n [-8, -2, 1, 0],\n [2, -4, 0, 5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 841 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, 2, -2, 0],\n [2, -8, 6, 1],\n [-2, 6, 6, 6],\n [0, 1, 6, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 448 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-8, 6, 0, 8],\n [0, 6, -4, -3],\n [0, 0, -11, -4],\n [0, 0, 0, 5]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 640 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-7, -8, 8, -1],\n [0, 6, 9, -6],\n [0, 0, -5, -4],\n [0, 0, 0, 11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 310 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, 0, 1, 6],\n [0, -6, 6, -9],\n [1, 6, -12, 4],\n [6, -9, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 877 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, 11, -2, -5],\n [0, -12, 10, 12],\n [0, 0, -2, -2],\n [0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 576 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[5, 6, 5, 6],\n [-1, -10, -9, -3],\n [-12, 9, -8, 6],\n [-11, 1, 8, -4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 969 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, -3, 4, -7],\n [-3, -12, 2, 4],\n [4, 2, 4, -6],\n [-7, 4, -6, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 704 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-5, 6, -10, -3],\n [6, -12, 6, 10],\n [-10, 6, -11, 3],\n [-3, 10, 3, -11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 712 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-5, 5, -6, 1],\n [5, -8, -2, -2],\n [-6, -2, -8, 2],\n [1, -2, 2, -4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 752 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-12, -12, 7, 1],\n [8, 3, 5, -3],\n [2, 4, -6, 2],\n [-6, 6, 3, -10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 254 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[4, -6, -10, -5],\n [0, -6, 0, 2],\n [0, 0, -2, -9],\n [0, 0, 0, -4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 808 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[12, -2, 3, 0],\n [6, -1, -2, 12],\n [10, -5, -5, -1],\n [10, 2, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 314 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[7, 1, -11, -7],\n [0, 3, 3, 1],\n [0, 0, 6, -9],\n [0, 0, 0, -12]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 488 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[6, 0, -9, 1],\n [0, 5, 11, -7],\n [0, 0, 8, -2],\n [0, 0, 0, -4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-5, -1, 2, -9],\n [-1, -1, -3, 10],\n [-4, -3, 12, -6],\n [2, 10, 10, 11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 21 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[7, -1, 0, -6],\n [-1, 1, 2, -2],\n [0, 2, 9, -6],\n [-6, -2, -6, -12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 304 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-3, -8, 2, -2],\n [-8, 11, 1, -2],\n [2, 1, 12, -5],\n [-2, -2, -5, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 478 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-4, 8, 3, 0],\n [8, 12, -3, 8],\n [3, -3, -5, -4],\n [0, 8, -4, 10]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 296 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, -2, 6, -2],\n [-2, -4, 2, 0],\n [6, 2, 10, 10],\n [-2, 0, 10, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 360 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[10, 10, -12, 0],\n [0, -1, 6, 6],\n [0, 0, 11, 9],\n [0, 0, 0, 5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 450 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[0, 0, -11, 0],\n [-12, 8, 6, 9],\n [-11, 5, 7, 4],\n [-7, -7, -11, 9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 300 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, 3, 4, -1],\n [3, -12, -11, 0],\n [4, -11, 6, -3],\n [-1, 0, -3, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 647 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, -7, 2, -5],\n [-6, 3, 8, -3],\n [-2, 7, 9, 8],\n [4, 2, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 248 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-11, -3, 1, 7],\n [10, -11, 11, 10],\n [-4, -6, -3, -9],\n [-12, -12, 2, -3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 715 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[4, -6, 1, -7],\n [0, -10, 10, -6],\n [0, 0, 8, -5],\n [0, 0, 0, 10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 800 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[7, 9, 2, -1],\n [11, -2, 8, -9],\n [-9, 7, 11, -6],\n [5, 1, 5, 0]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 578 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-2, -4, -8, 0],\n [-4, -7, -7, -5],\n [-8, -7, -12, -11],\n [0, -5, -11, 11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 604 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, 10, -9, -3],\n [-10, 1, -11, 4],\n [-2, -5, -7, -5],\n [-11, 7, 11, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 405 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[12, 6, 4, -4],\n [6, -8, 0, -1],\n [4, 0, -6, 0],\n [-4, -1, 0, 0]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 32 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, -4, 11, -9],\n [-1, 8, -2, -3],\n [2, 2, -1, 5],\n [8, -4, 11, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 512 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-6, -10, 11, 1],\n [-8, -10, 2, -7],\n [11, 12, -3, -3],\n [10, 8, -12, 9]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 526 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-3, 8, 2, 5],\n [8, -8, 8, 0],\n [2, 8, -5, -2],\n [5, 0, -2, -4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 640 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 12, 1, 6],\n [0, 9, -3, -5],\n [0, 0, -3, -1],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 270 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-2, -10, 10, 6],\n [0, 3, 0, 6],\n [-2, -8, 7, -3],\n [-10, 2, -3, 6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 830 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, 3, -2, -1],\n [0, 12, 4, -10],\n [0, 0, 1, 10],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 96 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, -2, -5, -6],\n [-2, 1, -6, 2],\n [-5, -6, -2, -3],\n [-6, 2, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 636 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, -6, 2, -8],\n [0, -4, -8, 2],\n [0, 0, -12, -5],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 424 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, -6, -1, 4],\n [-6, 1, -3, 0],\n [-1, -3, 4, 2],\n [4, 0, 2, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 707 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, 0, -2, -3],\n [0, 8, 11, 4],\n [-2, 11, -2, 2],\n [-3, 4, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 169 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[4, -4, 2, -1],\n [1, -6, 5, -7],\n [-12, 12, -10, -4],\n [8, 4, -7, -6]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 412 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, -4, 8, 0],\n [-4, -7, -4, 7],\n [8, -4, 0, 6],\n [0, 7, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 504 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[6, -4, -6, 2],\n [-4, -12, -2, 7],\n [-6, -2, -8, -10],\n [2, 7, -10, -8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 460 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-3, -11, 4, -11],\n [-3, 0, 9, 0],\n [-1, -8, 4, -10],\n [8, 2, 6, 10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 856 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, 10, -6, 7],\n [4, 6, -1, -4],\n [10, -10, 4, -3],\n [-9, 12, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 892 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, 2, 5, -11],\n [-7, 6, 10, 8],\n [-4, -12, -8, -2],\n [1, -7, -11, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 82 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, -10, 2, -7],\n [0, 1, -5, -5],\n [0, 0, -4, -1],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 920 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[2, -2, 10, -10],\n [0, -2, -11, 6],\n [0, 0, -3, -2],\n [0, 0, 0, -1]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 988 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, 1, 10, 7],\n [-4, -5, 1, 11],\n [-10, -12, -5, -2],\n [-5, -11, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-9, 12, -7, 5],\n [-2, 3, -9, 8],\n [-7, 8, -8, 6],\n [7, -10, 1, 4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 381 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-2, 10, 4, 3],\n [0, 1, 9, -11],\n [0, 0, -8, -11],\n [0, 0, 0, -9]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 856 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, 0, 6, 4],\n [0, 7, 0, 7],\n [6, 0, -2, -6],\n [4, 7, -6, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 744 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, 1, -4, 10],\n [1, 0, 0, 9],\n [-4, 0, 0, -4],\n [10, 9, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 24 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, 3, 2, 0],\n [0, -11, -2, 10],\n [0, 0, -10, -11],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-9, 6, 6, -5],\n [6, 1, 4, 7],\n [6, 4, 11, -8],\n [-5, 7, -8, 9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 413 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[5, 2, -2, -1],\n [0, -1, -4, 1],\n [0, 0, 11, -6],\n [0, 0, 0, -5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 275 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, -5, -6, -9],\n [-5, 5, -4, 1],\n [-6, -4, -2, -8],\n [-9, 1, -8, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 264 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, 7, 3, 0],\n [7, 0, -4, 2],\n [3, -4, -8, -6],\n [0, 2, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 904 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, 3, -3, 2],\n [-3, -5, -9, -10],\n [10, -2, -10, 6],\n [8, 7, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 584 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[2, 0, 4, -10],\n [0, 12, -5, 8],\n [0, 0, -8, -12],\n [0, 0, 0, 12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 696 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[11, 4, 7, 3],\n [0, -9, -5, -11],\n [0, 0, -1, -8],\n [0, 0, 0, 1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 99 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, 6, 7, 10],\n [-6, 9, 10, 8],\n [0, -6, 8, -1],\n [11, -10, -9, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 251 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 5, -8, 12],\n [0, -6, 4, 6],\n [0, 0, 8, 3],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 832 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-7, 12, 0, -11],\n [0, -10, 6, 8],\n [0, 0, -12, 10],\n [0, 0, 0, 3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 480 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-6, -5, -11, 8],\n [0, 7, 11, 10],\n [0, 0, -9, -11],\n [0, 0, 0, -6]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 732 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-4, -5, 0, 5],\n [0, 8, 12, -12],\n [0, 0, 4, -10],\n [0, 0, 0, 2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 744 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-5, 11, -10, -1],\n [10, -12, -6, 5],\n [-8, -5, 10, -7],\n [-11, -9, 12, -2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 32 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[10, 2, 8, -8],\n [0, 8, -2, -2],\n [0, 0, 3, -10],\n [0, 0, 0, 8]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 920 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-7, 2, -10, -7],\n [0, 3, 1, -4],\n [0, 0, 4, -3],\n [0, 0, 0, 1]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 916 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-1, -8, 2, -4],\n [-8, -3, 2, -1],\n [2, 2, 3, 6],\n [-4, -1, 6, 2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 77 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, -6, -7, 1],\n [-10, -4, -4, -6],\n [-6, -3, -3, 10],\n [-4, -9, -2, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 862 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[9, 5, 4, 4],\n [5, 2, 1, 12],\n [4, 1, -7, 0],\n [4, 12, 0, -1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 824 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-5, -3, 2, -6],\n [-3, 11, -10, 0],\n [2, -10, -1, 6],\n [-6, 0, 6, 6]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 716 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[2, -3, 4, 1],\n [-3, -4, 4, -8],\n [4, 4, -3, 6],\n [1, -8, 6, 8]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 64 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[2, -5, 1, 8],\n [-1, -1, 7, -11],\n [9, -10, -5, 3],\n [4, 4, -11, 10]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 212 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, 7, 8, 4],\n [4, 6, -6, 3],\n [-5, 9, 5, 4],\n [-11, 5, -12, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 219 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-7, -5, -2, 7],\n [-5, -9, -6, 7],\n [-2, -6, -8, -8],\n [7, 7, -8, 7]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 808 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[0, 7, 8, 5],\n [0, 2, -6, -9],\n [7, 4, -6, -7],\n [0, 2, 5, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 95 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[2, 5, -9, -10],\n [-2, -8, -5, -7],\n [-3, 5, -1, 3],\n [-4, -3, 11, 9]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 573 | MATH |
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