messages listlengths 1 1 | ground_truth stringlengths 1 3 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Determine the value of det(A) where A =\n[[-10, -1, -3, -9],\n [-3, -4, 3, 5],\n [-8, -9, 3, 4],\n [9, 0, -10, -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"
}
] | 195 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-11, 2, 1, 0],\n [2, 6, -2, -6],\n [1, -2, -2, -6],\n [0, -6, -6, -6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 184 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[3, -2, 8, 0],\n [-2, -8, -4, 2],\n [8, -4, 0, -10],\n [0, 2, -10, 0]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 896 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[4, -9, -3, 6],\n [-10, -12, 11, -3],\n [0, -12, 11, -11],\n [5, 4, 6, -1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 658 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-4, -5, 4, 2],\n [-5, -12, -2, -4],\n [4, -2, -1, 4],\n [2, -4, 4, -4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 700 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[12, 2, 4, 2],\n [2, 6, -4, 4],\n [4, -4, -4, 6],\n [2, 4, 6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 432 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 4, -2, 3],\n [1, -3, 7, -1],\n [-3, -1, 12, 0],\n [-3, -5, -8, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 358 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, -8, -1, -7],\n [1, -5, -2, -4],\n [9, 8, 8, 1],\n [1, -11, 4, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 783 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[4, 6, -10, -6],\n [6, 11, 8, 11],\n [8, -10, 2, 10],\n [7, -7, 10, -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"
}
] | 840 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, -8, 8, 4],\n [-8, 11, 2, 3],\n [8, 2, -12, 5],\n [4, 3, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 780 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[1, 5, 8, 0],\n [5, 1, 3, -5],\n [8, 3, 1, 8],\n [0, -5, 8, 2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 357 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[3, -6, -10, 0],\n [-6, -1, -11, 0],\n [-10, -11, -5, 10],\n [0, 0, 10, -2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 676 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[10, -2, 2, 4],\n [3, -7, 9, -3],\n [-1, 0, -5, 3],\n [0, -9, 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"
}
] | 642 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-9, -9, 9, -12],\n [0, -12, -3, -4],\n [0, 0, 7, 3],\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"
}
] | 268 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[6, -8, 4, 9],\n [0, 4, 9, -2],\n [0, 0, -3, -10],\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"
}
] | 928 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[4, 12, -4, -12],\n [1, 12, -10, 5],\n [2, 8, -10, 5],\n [2, 5, -5, 12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 248 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, -9, -9, 0],\n [0, -5, -5, -7],\n [0, 0, -8, 0],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 800 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[12, 2, 6, -6],\n [2, 12, -8, 0],\n [6, -8, 12, 2],\n [-6, 0, 2, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 872 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-2, 7, 9, -7],\n [0, 6, 11, -6],\n [0, 0, 8, 4],\n [0, 0, 0, -7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 672 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-6, -9, 1, -8],\n [0, -9, 1, 8],\n [0, 0, -11, 8],\n [0, 0, 0, 11]]? 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": "What is the determinant of the matrix:\n[[-4, 1, 1, -2],\n [1, 4, 0, 0],\n [1, 0, -8, -8],\n [-2, 0, -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"
}
] | 872 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[12, -3, -4, -8],\n [0, -12, 1, -9],\n [8, 4, 7, -7],\n [-3, -1, 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"
}
] | 920 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, -8, 6, -6],\n [0, 2, -7, 7],\n [0, 0, 2, -3],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 64 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-7, -1, 7, -7],\n [4, -5, 12, -3],\n [-11, -9, 4, -1],\n [5, -12, 12, 6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 956 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 10, -1, -2],\n [0, 11, -6, 1],\n [0, 0, 11, -6],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 541 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, -2, -2, 0],\n [-2, -1, -6, 8],\n [-2, -6, 3, 5],\n [0, 8, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 749 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, 7, -5, 6],\n [-4, 10, 6, -10],\n [0, -12, -2, 4],\n [-7, 6, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 380 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-1, -3, -8, 5],\n [-3, 2, 0, 0],\n [-8, 0, -1, 10],\n [5, 0, 10, 11]]\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"
}
] | 263 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, 9, 7, -2],\n [9, 12, -6, 6],\n [7, -6, 11, -8],\n [-2, 6, -8, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 410 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-10, -4, -5, 4],\n [-4, 3, 0, 7],\n [-5, 0, -10, 2],\n [4, 7, 2, -11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 194 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-9, 9, -5, 5],\n [-9, -8, 8, -8],\n [-9, -2, -3, 1],\n [1, 5, -9, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 385 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-2, -10, -2, -1],\n [0, 12, 4, 6],\n [0, 0, 1, 12],\n [0, 0, 0, 11]]\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"
}
] | 736 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[6, -4, -6, 5],\n [-4, 8, -4, 1],\n [-6, -4, -11, 6],\n [5, 1, 6, 9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 982 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[0, 4, -3, 0],\n [4, 2, 10, 3],\n [-3, 10, 5, 3],\n [0, 3, 3, -4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 793 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[4, 2, -2, 4],\n [2, 8, 0, -6],\n [-2, 0, 1, -1],\n [4, -6, -1, 11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 880 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-8, 0, -1, 12],\n [-6, -4, -9, -10],\n [3, 2, 0, 11],\n [-8, -2, -10, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 720 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, -3, 7, 7],\n [0, -12, -2, 1],\n [0, 0, 3, -12],\n [0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 416 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[9, 0, -2, 3],\n [0, -9, -5, -2],\n [-2, -5, 12, -3],\n [3, -2, -3, 3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 283 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-12, 2, 8, 0],\n [2, 8, -10, -4],\n [8, -10, 3, -4],\n [0, -4, -4, -6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 120 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, -4, 5, 11],\n [0, -4, 7, -1],\n [0, 0, -9, 4],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 216 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, 4, 3, 4],\n [4, 2, 1, -8],\n [3, 1, -5, 10],\n [4, -8, 10, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 492 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-8, 9, -2, 12],\n [8, 3, -10, -5],\n [4, -2, 9, 12],\n [-10, 6, 0, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 610 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-8, -7, -3, 8],\n [-7, 2, 2, -4],\n [-3, 2, -3, -2],\n [8, -4, -2, 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"
}
] | 600 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[7, -2, 6, 2],\n [9, -4, 11, 0],\n [-3, -9, -8, -8],\n [-12, 5, -11, 10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 286 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, -2, 0, 0],\n [-2, -7, 6, -7],\n [0, 6, -12, 4],\n [0, -7, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 308 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[4, -9, -10, 11],\n [0, 1, 11, -1],\n [0, 0, -11, -9],\n [0, 0, 0, -6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 264 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-12, -2, -2, 1],\n [-2, 7, 1, 10],\n [-2, 1, -2, -2],\n [1, 10, -2, -5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 335 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-3, -11, -5, 1],\n [0, -7, -8, 9],\n [0, 0, 12, -4],\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"
}
] | 984 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-5, 0, 4, -4],\n [0, -2, -1, 3],\n [4, -1, -9, -8],\n [-4, 3, -8, -4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 191 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[5, 8, -1, -9],\n [0, -4, -4, -5],\n [0, 0, -4, -8],\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"
}
] | 920 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[3, -7, -10, -8],\n [10, -7, -7, -2],\n [3, 5, 1, -10],\n [7, -5, -10, -6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 950 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[2, -1, -1, 8],\n [-1, 4, -10, 4],\n [-1, -10, 1, -6],\n [8, 4, -6, 5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 439 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[3, -6, -4, 0],\n [-6, -6, 2, -1],\n [-4, 2, 4, -4],\n [0, -1, -4, -4]]\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"
}
] | 868 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, 3, 8, -4],\n [3, 12, 2, 0],\n [8, 2, -6, 0],\n [-4, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 96 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[9, 2, -10, 5],\n [0, -12, -6, -4],\n [0, 0, -8, -6],\n [0, 0, 0, -8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 88 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-7, -8, 6, 8],\n [-9, 3, -10, -4],\n [-7, -9, 7, 10],\n [-10, 7, -12, -12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 232 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-3, 6, 9, 1],\n [0, -2, 3, -7],\n [0, 0, 10, -6],\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"
}
] | 720 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[1, -4, -4, -3],\n [0, 11, -12, -4],\n [0, 0, -8, 4],\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"
}
] | 176 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[7, 5, 11, 9],\n [5, 9, -4, 0],\n [11, -4, 12, 0],\n [9, 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"
}
] | 698 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[5, 8, 7, 10],\n [0, -6, 2, 11],\n [0, 0, -2, 3],\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"
}
] | 940 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[8, 6, -2, 0],\n [6, -3, 0, 3],\n [-2, 0, -5, -2],\n [0, 3, -2, 0]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 492 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-9, 4, -4, 5],\n [-5, -2, -5, -5],\n [3, 7, 2, 12],\n [4, -1, 11, -8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 877 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[7, -2, -5, -11],\n [0, -9, -3, -3],\n [0, 0, -8, -11],\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"
}
] | 544 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[9, 9, 6, -9],\n [-3, -9, -2, 3],\n [-6, -6, -9, -10],\n [12, -10, -10, 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"
}
] | 142 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, -10, -2, 3],\n [-8, -8, 7, 4],\n [-9, 12, -2, -3],\n [3, -8, -8, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 964 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[0, -6, -7, -9],\n [-1, 11, -12, -12],\n [1, -4, 12, -1],\n [-12, -3, -6, 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"
}
] | 901 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, 4, -2, 0],\n [4, -12, 5, -3],\n [-2, 5, -4, 3],\n [0, -3, 3, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 740 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-1, 1, 2, 8],\n [0, -1, -5, 0],\n [0, 0, -11, -11],\n [0, 0, 0, -7]]? Round to the nearest integer, then express your answer 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[[-9, 6, 4, -12],\n [6, 11, 4, 2],\n [4, 4, -10, -6],\n [-12, 2, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 166 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-5, 1, 10, 3],\n [0, 8, -7, -10],\n [0, 0, -10, 12],\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"
}
] | 200 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[4, 7, 11, 5],\n [10, 1, 7, -5],\n [4, 0, -8, 8],\n [0, -8, 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"
}
] | 288 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-4, -9, 8, 0],\n [0, 7, 2, -10],\n [0, 0, -2, 12],\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"
}
] | 504 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 7, 12, -4],\n [7, -4, 2, 4],\n [12, 2, -11, -6],\n [-4, 4, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 174 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, -12, -1, 11],\n [0, -3, 9, -6],\n [0, 0, -10, 9],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 640 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, -12, -6, -6],\n [-12, 3, 0, 6],\n [-6, 0, -10, 8],\n [-6, 6, 8, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 798 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[5, 4, -1, -9],\n [4, 7, -4, -2],\n [-1, -4, 5, 8],\n [-9, -2, 8, -6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 701 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 1, 2, 11],\n [-4, 5, 0, 8],\n [-8, 11, -12, -10],\n [4, -4, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 600 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[3, -4, 4, 6],\n [-4, -8, 0, 10],\n [4, 0, -8, -4],\n [6, 10, -4, -4]]\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": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, 2, -8, 11],\n [0, -4, 3, -7],\n [0, 0, -6, -2],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 704 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[8, -4, 9, 3],\n [0, 8, 0, 7],\n [0, 0, 9, -1],\n [0, 0, 0, -1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 424 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[4, 7, 6, 8],\n [7, 2, -4, -2],\n [6, -4, 0, -6],\n [8, -2, -6, -12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 308 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[9, 2, 0, 1],\n [-3, 6, -10, -5],\n [8, 3, 9, 5],\n [7, 12, -5, -7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 518 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[12, 2, -12, -8],\n [0, -9, -11, -9],\n [0, 0, -10, 1],\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"
}
] | 200 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[9, -4, 0, 6],\n [-4, 2, 1, -10],\n [0, 1, -12, 8],\n [6, -10, 8, -12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 152 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-4, -12, 7, -1],\n [0, 7, -7, 1],\n [0, 0, -11, 1],\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"
}
] | 228 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-4, 9, -7, 4],\n [0, -10, 3, -2],\n [0, 0, 3, -6],\n [0, 0, 0, -7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 160 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-10, -11, -1, -1],\n [-11, 9, 4, 11],\n [-1, -4, -2, -3],\n [-5, 10, -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"
}
] | 2 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-11, 2, -2, 5],\n [0, -11, 12, -12],\n [0, 0, -5, -10],\n [0, 0, 0, 3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 185 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, 0, 4, -8],\n [0, 3, 7, 10],\n [4, 7, 4, -8],\n [-8, 10, -8, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 157 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-12, 5, 5, 5],\n [5, -7, -4, 4],\n [5, -4, -11, 3],\n [5, 4, 3, 12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 150 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[10, 0, 6, 4],\n [0, 6, 6, 0],\n [6, 6, -6, 5],\n [4, 0, 5, 10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 732 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-2, 10, 12, 8],\n [0, -3, 7, -3],\n [0, 0, 3, 0],\n [0, 0, 0, -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"
}
] | 820 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[0, 1, -8, -1],\n [6, -4, -6, -3],\n [7, 3, 6, -2],\n [7, 8, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 813 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-4, 10, -12, 2],\n [0, -9, 2, 5],\n [0, 0, -5, -9],\n [0, 0, 0, -12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 160 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[9, 0, -1, 0],\n [0, 7, 9, 0],\n [-1, 9, 12, 0],\n [0, 0, 0, 7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 140 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[11, -7, -9, -4],\n [4, 2, -1, -1],\n [4, 10, -10, 7],\n [-3, -6, 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"
}
] | 905 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[7, 1, -5, -6],\n [1, -1, -4, -1],\n [-5, -4, 2, -10],\n [-6, -1, -10, -5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 178 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, -2, -4, 4],\n [-2, 7, -6, -3],\n [-4, -6, 5, 5],\n [4, -3, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 452 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, 1, 4, -5],\n [9, 4, -2, 8],\n [-3, 6, 11, -3],\n [-4, 5, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 413 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[9, 0, -4, -10],\n [0, 10, -3, 2],\n [-4, -3, -12, -5],\n [-10, 2, -5, 6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 240 | MATH |
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