messages listlengths 1 1 | ground_truth stringclasses 992
values | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, -1, -10, -10],\n [0, -2, 9, 12],\n [0, 0, 6, -6],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 288 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, -4, -4, 1],\n [-4, 7, -4, -2],\n [-4, -4, 6, 1],\n [1, -2, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 33 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, 9, -12, 3],\n [0, 5, -1, -3],\n [0, 0, -12, -8],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 480 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-8, -12, -12, -3],\n [0, -3, 3, 10],\n [0, 0, 4, -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"
}
] | 944 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[7, 3, -12, 11],\n [0, -3, 7, -9],\n [0, 0, 7, 7],\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"
}
] | 323 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[11, -3, 5, -2],\n [-3, -7, 2, -10],\n [5, 2, 5, -6],\n [-2, -10, -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"
}
] | 150 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, 4, -7, -9],\n [0, -8, 3, 6],\n [0, 0, -3, 10],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 840 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[3, -11, -1, 3],\n [3, -11, -12, -8],\n [11, -6, -1, 9],\n [2, 4, 9, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 261 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[0, 9, -2, 4],\n [9, 12, -8, -6],\n [-2, -8, -8, 6],\n [4, -6, 6, 5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 292 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 6, 9, 9],\n [-6, -1, 11, 7],\n [-7, 7, -5, 7],\n [-4, 9, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 803 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[12, 11, -4, 10],\n [-1, 5, 0, -1],\n [-5, -7, -3, -8],\n [-11, 11, -12, 5]]? 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": "What is the determinant of the matrix:\n[[-1, -12, -8, -11],\n [0, 3, -6, -8],\n [0, 0, 9, -12],\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"
}
] | 892 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-8, 0, 1, -2],\n [0, -1, -4, 9],\n [0, 0, 8, -4],\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"
}
] | 680 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-6, 0, -11, -4],\n [0, -1, -10, -1],\n [0, 0, -3, -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"
}
] | 802 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-4, 3, 4, -12],\n [3, -2, 4, -3],\n [4, 4, -2, 3],\n [-12, -3, 3, -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"
}
] | 841 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-5, 12, 5, -7],\n [0, -11, 3, 3],\n [0, 0, 8, 5],\n [0, 0, 0, 6]]\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": "What is the determinant of the matrix:\n[[11, -1, 6, -10],\n [5, -7, 6, -1],\n [-6, -4, 4, 6],\n [-5, -2, 2, 8]]? 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[[-9, -2, -4, -5],\n [-2, 7, 4, 12],\n [-4, 4, 11, 8],\n [-5, 12, 8, -6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 41 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, -3, 9, 0],\n [11, 12, -2, 5],\n [8, -10, 12, -10],\n [-7, -1, -8, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 24 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[7, -1, 0, -11],\n [0, -10, -5, 12],\n [0, 0, -9, 12],\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"
}
] | 700 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, 7, 8, 4],\n [0, -11, 2, -12],\n [0, 0, 10, 0],\n [0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 900 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-3, 2, 1, 0],\n [7, -10, 4, 6],\n [-9, -11, 12, 6],\n [6, 10, 7, 1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 383 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[12, 0, 6, 5],\n [0, -4, 0, -9],\n [6, 0, 7, 2],\n [5, -9, 2, -9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 252 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, -3, 2, -2],\n [-3, 9, 8, -6],\n [2, 8, 0, -2],\n [-2, -6, -2, -11]]\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[[5, 7, 12, 11],\n [-6, 5, -2, 2],\n [-5, 6, 12, 6],\n [-3, 5, -12, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 924 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, -6, 0, 4],\n [-6, 7, 2, 2],\n [0, 2, -11, 0],\n [4, 2, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 448 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, -7, 4, -10],\n [-7, -9, -1, -8],\n [4, -1, 9, 5],\n [-10, -8, 5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 189 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-5, 5, 4, -8],\n [0, 10, -1, -4],\n [0, 0, -1, 1],\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"
}
] | 400 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[12, -8, -2, 2],\n [-8, 0, -3, -2],\n [-2, -3, -11, -2],\n [2, -2, -2, -10]]? 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": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, 1, 11, 2],\n [-5, -6, -7, -6],\n [3, -5, -9, 1],\n [11, 12, 11, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 756 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[0, 7, 2, 2],\n [7, -12, -10, -4],\n [2, -10, 12, -5],\n [2, -4, -5, -3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 581 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[4, 1, 3, 9],\n [-9, -4, 10, -2],\n [-6, 3, -6, -4],\n [-5, -1, 12, 5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 679 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[12, 5, -12, -5],\n [-5, 9, -9, -12],\n [1, 12, 6, -11],\n [7, -4, 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"
}
] | 985 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[10, -7, 1, 1],\n [0, 2, -3, 9],\n [0, 0, 1, -5],\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"
}
] | 900 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-2, -10, 4, -5],\n [-10, -6, 1, 0],\n [4, 1, 9, 8],\n [-5, 0, 8, 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"
}
] | 387 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[7, 7, -1, -9],\n [0, -5, -6, 6],\n [0, 0, 5, 4],\n [0, 0, 0, 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"
}
] | 775 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-1, 1, -11, 2],\n [12, 2, -12, -8],\n [12, 2, 12, 11],\n [0, 0, -2, -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"
}
] | 156 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[6, 4, 1, 2],\n [4, -3, 0, -6],\n [1, 0, -2, -8],\n [2, -6, -8, -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"
}
] | 814 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-10, -5, -6, 1],\n [-5, -3, 4, -6],\n [-6, 4, 7, 2],\n [1, -6, 2, 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"
}
] | 770 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, -1, -7, 2],\n [0, -9, 1, -4],\n [0, 0, -11, 0],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 594 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[10, 6, 8, 7],\n [-4, -3, -11, 8],\n [7, -12, -11, -7],\n [11, -6, 8, -2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 463 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[9, 12, 10, 1],\n [0, -2, -3, 8],\n [0, 0, -10, -8],\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"
}
] | 460 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[5, 4, 5, -12],\n [0, -7, 7, 3],\n [0, 0, -10, -4],\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"
}
] | 150 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-2, -11, 10, 4],\n [0, -5, 10, -2],\n [0, 0, 6, -11],\n [0, 0, 0, -2]]\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"
}
] | 880 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, -1, 2, 2],\n [-1, 10, -8, 0],\n [2, -8, -6, 0],\n [2, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 118 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, -1, 7, -9],\n [-11, 1, 9, 12],\n [0, -12, -11, -10],\n [-3, -8, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 694 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, -8, -6, 2],\n [-8, -11, 3, 2],\n [-6, 3, 6, -4],\n [2, 2, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 750 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-1, -12, -4, 8],\n [-12, -10, -9, 2],\n [-4, -9, -10, 1],\n [8, 2, 1, -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"
}
] | 518 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-5, 0, 6, 3],\n [0, 11, 2, 5],\n [6, 2, 11, 4],\n [3, 5, 4, -1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 907 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, -10, 4, -6],\n [-10, 1, 0, -6],\n [4, 0, -2, 4],\n [-6, -6, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 840 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[9, -1, 0, -5],\n [-1, 2, -3, 3],\n [0, -3, 11, 0],\n [-5, 3, 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"
}
] | 8 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[12, 2, -12, -8],\n [2, 6, -10, -1],\n [-12, -10, -2, -4],\n [-8, -1, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 568 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, 4, 8, 12],\n [5, -12, -5, 7],\n [-4, -4, -10, -4],\n [0, -3, 1, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 352 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-5, 12, 11, 5],\n [0, 7, 9, -7],\n [0, 0, 11, -1],\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"
}
] | 155 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, -1, -7, 4],\n [-1, 4, 1, -10],\n [-7, 1, -12, 0],\n [4, -10, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 207 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[11, -1, 12, -6],\n [0, 11, -2, -3],\n [0, 0, 6, -3],\n [0, 0, 0, -2]]\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"
}
] | 548 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, 9, -12, -9],\n [0, -5, -2, 6],\n [0, 0, -1, 2],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 940 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-11, 3, 0, -8],\n [0, 11, -9, -9],\n [0, 0, -1, -9],\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"
}
] | 89 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[12, 2, -2, 8],\n [2, 9, 5, -2],\n [-2, 5, 8, -2],\n [8, -2, -2, -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"
}
] | 680 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, -1, 4, 6],\n [-1, 7, 0, 4],\n [4, 0, 10, 0],\n [6, 4, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 194 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-9, 1, 6, 12],\n [6, 3, -2, -2],\n [11, -3, 12, 9],\n [-9, 9, -4, -12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 254 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-6, -8, 0, -4],\n [-8, -8, -6, 6],\n [0, -6, -11, -2],\n [-4, 6, -2, -8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 864 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[11, -4, -1, -12],\n [0, 10, 3, 8],\n [0, 0, 6, -10],\n [0, 0, 0, -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"
}
] | 380 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, -4, 3, 7],\n [0, -8, -2, 5],\n [0, 0, -7, 2],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 672 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[2, -7, 6, 2],\n [-7, -1, 6, 5],\n [6, 6, 9, 6],\n [2, 5, 6, 8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 598 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[3, -2, -9, -9],\n [-2, -11, -4, 6],\n [-9, -4, -6, -5],\n [-9, 6, -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"
}
] | 574 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-3, -2, -2, 10],\n [-2, 2, 8, -7],\n [-2, 8, -1, 8],\n [10, -7, 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"
}
] | 921 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, 11, 3, 7],\n [12, -12, -2, -6],\n [10, -6, -7, -7],\n [-12, -6, 9, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 656 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[8, 11, 2, -10],\n [7, -8, 1, 12],\n [9, 10, 5, -3],\n [-5, 10, 10, -1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 27 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-10, -4, 1, 6],\n [0, -11, 7, 12],\n [0, 0, -11, -10],\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"
}
] | 480 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-2, 2, -1, -4],\n [2, 7, 1, 2],\n [-1, 1, -6, -1],\n [-4, 2, -1, -3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 469 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, 0, -2, -2],\n [0, -4, -1, 0],\n [-2, -1, 1, 5],\n [-2, 0, 5, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 842 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[3, 12, -3, -1],\n [10, 10, -5, -9],\n [3, 12, -5, 5],\n [9, -2, 10, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 312 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[3, -5, -6, 3],\n [-5, 8, 6, 5],\n [-6, 6, -12, -4],\n [3, 5, -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": "What is the determinant of the matrix:\n[[-3, 3, 4, -4],\n [3, 9, -2, -6],\n [4, -2, 3, 0],\n [-4, -6, 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"
}
] | 196 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[6, 12, 8, 6],\n [-8, -10, 4, 1],\n [11, 10, -8, 1],\n [-11, 9, -8, -3]]\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"
}
] | 664 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[0, 0, 2, -2],\n [0, -1, -7, -2],\n [2, -7, 7, -4],\n [-2, -2, -4, -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"
}
] | 284 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-1, -4, -12, 1],\n [0, -5, -9, 12],\n [0, 0, -4, 4],\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"
}
] | 980 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-2, 9, 11, 9],\n [-8, 6, 10, -3],\n [6, -9, 7, 4],\n [-9, -12, 9, -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"
}
] | 562 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[0, -1, 0, -3],\n [-1, -5, -3, -2],\n [0, -3, -11, -10],\n [-3, -2, -10, 7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 715 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[11, 2, 5, -3],\n [0, -4, 2, -8],\n [0, 0, 1, -9],\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"
}
] | 868 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, -11, -7, 11],\n [-12, 6, 3, -11],\n [7, -10, -3, 6],\n [8, 4, 10, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 785 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[2, 9, 5, 7],\n [0, 7, -11, 7],\n [0, 0, 10, -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"
}
] | 140 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[9, -1, 3, -9],\n [0, -8, -8, 8],\n [0, 0, 3, -11],\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"
}
] | 408 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, -10, 0, 2],\n [-10, 9, -2, 2],\n [0, -2, 2, 0],\n [2, 2, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 288 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-1, 4, -12, 2],\n [4, 10, -8, 7],\n [-12, -8, -2, 8],\n [2, 7, 8, -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"
}
] | 726 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[7, -7, 8, -12],\n [-2, 4, 3, 1],\n [-6, -6, 7, 1],\n [2, 11, -3, 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"
}
] | 570 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[9, 5, -5, -1],\n [10, 7, -2, -7],\n [-4, -9, 12, -10],\n [-3, -8, -5, -9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 324 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[6, 0, -2, -6],\n [0, 10, 1, -8],\n [-2, 1, 9, 8],\n [-6, -8, 8, -2]]\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"
}
] | 112 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, -8, 3, 9],\n [2, 8, -4, 0],\n [-3, -6, -4, 4],\n [0, 2, 4, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 96 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-2, 2, 7, 0],\n [2, -5, 6, 6],\n [7, 6, -11, -3],\n [0, 6, -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"
}
] | 178 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-9, 6, 8, -2],\n [6, -11, 6, 8],\n [8, 6, 4, 8],\n [-2, 8, 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"
}
] | 664 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-5, 2, 2, -7],\n [-11, -7, 10, -5],\n [1, -1, -4, -7],\n [-11, -5, 1, 3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 730 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, -12, 9, 7],\n [8, -10, -12, 6],\n [10, 11, -9, -11],\n [0, -7, 10, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 162 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, -1, 11, -1],\n [0, 8, -12, 9],\n [0, 0, -8, -1],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 232 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[8, 4, 12, -1],\n [0, -2, 1, 12],\n [0, 0, -12, 9],\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"
}
] | 808 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[2, -7, 4, 8],\n [-7, 11, 4, 7],\n [4, 4, 1, 4],\n [8, 7, 4, 12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 978 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[11, -2, -2, 2],\n [-2, -7, 0, 8],\n [-2, 0, -1, -2],\n [2, 8, -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"
}
] | 535 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[7, 11, -12, 4],\n [0, 7, 12, 1],\n [0, 0, -4, 8],\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"
}
] | 960 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, -12, -4, -6],\n [0, 5, 9, -12],\n [12, -12, -7, -7],\n [-3, 8, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 710 | MATH |
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