messages listlengths 1 1 | ground_truth stringlengths 1 3 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Compute |A| for the matrix A =\n[[11, 2, -3, 4],\n [2, 5, -2, 7],\n [-3, -2, -12, -2],\n [4, 7, -2, -2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 27 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, -6, 2, -8],\n [-6, -11, 4, 2],\n [2, 4, 0, -7],\n [-8, 2, -7, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 671 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, 2, -1, 4],\n [-3, -6, -4, 1],\n [2, 11, 0, 11],\n [-2, 2, 8, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 513 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[6, 7, 2, 10],\n [-6, -2, 12, -10],\n [3, -5, -6, 8],\n [-11, 6, 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"
}
] | 400 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-6, 12, 12, -1],\n [0, 3, -8, 4],\n [0, 0, 11, -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"
}
] | 376 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-5, 8, -2, -3],\n [8, -1, 6, -9],\n [-2, 6, 10, -10],\n [-3, -9, -10, -12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 552 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, -8, 3, 6],\n [-8, 0, -8, 5],\n [3, -8, 8, -1],\n [6, 5, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 737 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, -1, -2, -7],\n [0, 7, 0, 8],\n [0, 0, -12, -9],\n [0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 328 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, 4, 2, 4],\n [4, 5, -6, 2],\n [2, -6, -3, 2],\n [4, 2, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 873 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[3, -2, -6, 10],\n [-2, 12, 4, -1],\n [-6, 4, -4, 6],\n [10, -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"
}
] | 584 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-10, -2, -2, -2],\n [-2, 8, -4, 0],\n [-2, -4, -10, -6],\n [-2, 0, -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"
}
] | 896 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, 3, -4, 8],\n [0, -11, 6, 8],\n [0, 0, -2, 7],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 822 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, 2, 6, -10],\n [2, 3, -6, -2],\n [6, -6, 10, -7],\n [-10, -2, -7, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 981 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-12, 1, 11, 11],\n [3, -10, -12, 1],\n [-10, -5, -11, -9],\n [8, -1, -10, 10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 932 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-1, 4, 8, -2],\n [4, 4, -10, -3],\n [8, -10, 0, -10],\n [-2, -3, -10, 0]]\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"
}
] | 496 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, 7, -5, 5],\n [-8, 10, -4, 2],\n [-4, -2, 12, 3],\n [-8, -3, -1, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 972 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, -6, -6, -2],\n [-6, -1, 6, -9],\n [-6, 6, 10, 10],\n [-2, -9, 10, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 572 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, 7, -1, 7],\n [0, 8, 8, 6],\n [0, 0, 8, -5],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 280 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[5, 0, -6, 6],\n [0, 3, 8, -2],\n [-6, 8, -12, 0],\n [6, -2, 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"
}
] | 752 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, -9, -8, -9],\n [0, -1, -6, -12],\n [0, 0, -3, 5],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 180 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, -4, 2, -9],\n [-4, -2, 1, 8],\n [2, 1, -1, -8],\n [-9, 8, -8, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 59 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[10, 6, 12, -12],\n [12, -10, -5, -7],\n [8, -6, 8, -5],\n [6, -1, -9, -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"
}
] | 226 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-12, -3, -11, -9],\n [-1, 3, -12, -3],\n [-8, 11, 7, 1],\n [3, -8, 0, 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"
}
] | 520 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, 11, 9, -1],\n [7, -2, -1, 5],\n [-5, -2, -5, -6],\n [-11, -7, 9, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 126 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[1, -9, -8, -10],\n [0, -6, -6, -5],\n [0, 0, -7, -5],\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"
}
] | 832 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, -9, 4, 9],\n [-2, 4, -5, -3],\n [0, -1, 9, 7],\n [4, -8, -10, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 930 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[9, -4, -5, 0],\n [-4, -3, 2, 2],\n [-5, 2, 6, 9],\n [0, 2, 9, -1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 434 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-11, -6, -2, 0],\n [-6, 0, -3, 3],\n [-2, -3, 2, -2],\n [0, 3, -2, -4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 306 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-9, -10, -10, -2],\n [10, 12, -2, 3],\n [-12, -9, 6, -9],\n [11, -4, -9, -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"
}
] | 935 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, 7, -3, -10],\n [0, -2, -9, 5],\n [0, 0, -7, -8],\n [0, 0, 0, -10]]\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[[7, 10, 4, 1],\n [10, 2, 6, -1],\n [4, 6, 6, -2],\n [1, -1, -2, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 246 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[8, -6, -4, 5],\n [-6, -6, -6, 0],\n [-4, -6, 10, 5],\n [5, 0, 5, -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"
}
] | 420 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, 4, 8, -3],\n [4, 11, 8, 1],\n [8, 8, -11, 3],\n [-3, 1, 3, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 529 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-7, 9, 8, 3],\n [0, 6, -9, -12],\n [0, 0, -3, 7],\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"
}
] | 496 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[8, 1, -1, 11],\n [11, -8, -8, 8],\n [7, -10, 8, -10],\n [-12, 1, -6, -10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 182 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-8, -7, -3, 8],\n [-7, -3, 8, -2],\n [-3, 8, 3, 2],\n [8, -2, 2, 2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 168 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[12, -5, -8, -12],\n [0, -7, 6, 4],\n [0, 0, 5, 6],\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"
}
] | 40 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[9, 1, -6, 3],\n [-10, -5, 4, 11],\n [-7, -9, -11, 9],\n [1, 6, 7, -8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 284 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-10, -6, 0, -4],\n [0, 6, 6, 4],\n [0, 0, -7, -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"
}
] | 40 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, 7, -4, -12],\n [12, 12, 2, 5],\n [10, 7, 5, -2],\n [2, 12, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 482 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, 10, 11, -11],\n [0, -12, 11, -2],\n [0, 0, 12, -11],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 456 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, 11, 2, 10],\n [6, -1, 10, -3],\n [6, -12, -1, 8],\n [-9, -6, -1, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 160 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-6, -4, 12, 10],\n [-1, -11, 10, 5],\n [0, 8, -12, -7],\n [-3, 0, -8, 11]]? 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": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, -10, 1, -3],\n [-8, 6, -7, -10],\n [-2, 8, 9, 11],\n [3, 2, -2, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 642 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[0, 2, -6, 2],\n [2, 7, 1, -6],\n [-6, 1, 8, 3],\n [2, -6, 3, -3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 548 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, 1, 12, -5],\n [-9, 0, -10, -1],\n [-12, -3, 12, 10],\n [-5, 9, -5, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 411 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[7, 4, -4, 2],\n [4, 8, 6, 0],\n [-4, 6, 2, 0],\n [2, 0, 0, 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"
}
] | 604 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, -4, -1, -3],\n [-12, -7, 9, -6],\n [8, 5, 9, 11],\n [-4, 8, 11, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 529 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-11, 6, -1, 7],\n [6, -10, -6, -2],\n [-1, -6, -12, 0],\n [7, -2, 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"
}
] | 674 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, 6, 6, 4],\n [0, 2, 8, 5],\n [0, 0, 4, 11],\n [0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 792 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-9, -4, 7, 1],\n [0, 12, 3, -2],\n [0, 0, 9, 7],\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"
}
] | 804 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-12, -3, 8, -2],\n [-3, 11, -2, -1],\n [8, -2, -11, 2],\n [-2, -1, 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"
}
] | 398 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, -4, -3, 5],\n [-11, 2, 2, -2],\n [-9, -2, -8, -12],\n [-1, 6, -4, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 404 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-7, 4, 10, 8],\n [4, -7, 0, 2],\n [10, 0, -10, -2],\n [8, 2, -2, -9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 458 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-8, 4, 2, 2],\n [0, -7, 11, -11],\n [0, 0, -4, 9],\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"
}
] | 568 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-9, -12, -5, -2],\n [-12, 12, -10, -3],\n [-7, -9, 5, -11],\n [-3, -7, -6, 7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 989 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[6, -11, 7, 5],\n [5, 10, -3, 5],\n [-9, 3, -9, 8],\n [11, 2, 4, -11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 916 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-7, -3, 4, 3],\n [0, 5, -4, 1],\n [0, 0, -8, -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"
}
] | 40 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[0, -2, -4, -6],\n [-2, -9, -4, -7],\n [-4, -4, 1, -6],\n [-6, -7, -6, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 976 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[12, -10, 5, -6],\n [0, -11, -3, -2],\n [0, 0, 9, 2],\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"
}
] | 60 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, 0, 7, -5],\n [-1, 3, -12, 3],\n [6, 4, 12, -12],\n [1, -2, -12, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 900 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[9, 4, 11, -5],\n [0, -4, -2, -2],\n [0, 0, 12, 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"
}
] | 136 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-5, -2, 12, 4],\n [0, -8, -2, 8],\n [0, 0, 2, 9],\n [0, 0, 0, -9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 280 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[3, 5, -10, -8],\n [0, -10, -1, -1],\n [0, 0, 10, -10],\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"
}
] | 200 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-8, -6, 8, -12],\n [0, -9, 8, -7],\n [0, 0, 1, 6],\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"
}
] | 928 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, -5, -2, -3],\n [0, 4, -5, 2],\n [0, 0, -6, 4],\n [0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 944 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-12, 8, -4, -12],\n [0, -1, -5, -2],\n [0, 0, 2, -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"
}
] | 928 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, 0, 0, 2],\n [0, -12, 0, -3],\n [0, 0, 1, 4],\n [2, -3, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 48 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, 11, -6, 0],\n [-1, -9, 9, 1],\n [-6, -6, 9, -2],\n [-7, 4, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 317 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-1, 2, -8, 5],\n [2, -8, -4, -3],\n [-8, -4, -1, 0],\n [5, -3, 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"
}
] | 831 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[5, 3, -8, 3],\n [0, -6, 1, -12],\n [0, 0, -5, -2],\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"
}
] | 200 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[10, 2, -7, 6],\n [0, 5, -4, -8],\n [0, 0, -9, -2],\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"
}
] | 900 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, 8, 4, -7],\n [0, -1, -8, 9],\n [-3, 4, 9, 3],\n [7, 6, 4, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 183 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[11, -3, 9, 4],\n [12, 11, 7, -7],\n [-10, 7, -4, 4],\n [-5, -5, -1, 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"
}
] | 148 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[5, 0, -8, 0],\n [0, 6, 4, 2],\n [-8, 4, 5, 8],\n [0, 2, 8, -9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 702 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-5, -2, -2, -6],\n [12, 1, -4, 2],\n [9, 7, 1, 9],\n [1, -8, -1, -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"
}
] | 998 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, -12, -6, -11],\n [0, 5, -1, -10],\n [0, 0, -4, 0],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 120 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-5, -8, 5, -4],\n [-8, 9, 2, 1],\n [5, 2, 8, 10],\n [-4, 1, 10, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 530 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[7, -2, 0, 2],\n [-2, 9, 1, 0],\n [0, 1, -3, -4],\n [2, 0, -4, -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"
}
] | 608 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[4, 8, -10, 6],\n [11, -3, -3, 5],\n [-1, 1, -4, -2],\n [-9, 4, -12, -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"
}
] | 280 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, -9, 10, 7],\n [0, 6, -5, -7],\n [0, 0, 6, -12],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 356 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[12, 7, -11, -5],\n [0, 5, -7, -1],\n [0, 0, 10, -6],\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"
}
] | 600 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, -4, -1, 9],\n [0, -9, -7, 0],\n [0, 0, 8, 2],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 248 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-12, 1, 5, -7],\n [-7, 7, -8, -12],\n [8, -12, 2, 11],\n [-3, -8, -8, 7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 181 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[12, 2, 2, 0],\n [2, -5, -7, -6],\n [2, -7, -9, 2],\n [0, -6, 2, -1]]\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[[-11, 2, 1, 5],\n [0, 9, -6, -5],\n [0, 0, 10, 2],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 910 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[12, 6, 5, 11],\n [-12, 2, 5, 2],\n [-2, -1, -7, 4],\n [0, -10, 5, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 68 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, 6, 11, 12],\n [0, -2, -10, 2],\n [0, 0, 1, -3],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 952 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, 5, 5, -12],\n [0, -3, 9, 8],\n [0, 0, 11, -8],\n [0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 733 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[6, -11, 9, 8],\n [2, 9, -10, 8],\n [-1, -8, -11, 3],\n [-5, 5, 3, -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"
}
] | 343 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[7, -2, 6, 0],\n [-2, 3, 1, 10],\n [6, 1, 9, 2],\n [0, 10, 2, 10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 132 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-4, 10, -2, 8],\n [0, -1, 5, 6],\n [0, 0, 2, 0],\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"
}
] | 952 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-6, 0, -10, -3],\n [0, 7, 6, 8],\n [-10, 6, -7, 8],\n [-3, 8, 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"
}
] | 657 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, -9, -1, 0],\n [0, 1, 2, -1],\n [0, 0, -2, -9],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 998 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[8, -3, 5, 3],\n [0, 5, -4, 8],\n [0, 0, 7, -7],\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"
}
] | 40 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, -6, -9, 4],\n [-6, 3, 4, -4],\n [-9, 4, 11, -4],\n [4, -4, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 992 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, 12, 0, 0],\n [0, 1, -11, -1],\n [0, 0, -12, 9],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 36 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-4, 1, 10, 2],\n [0, 12, -1, -9],\n [0, 0, 5, -6],\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"
}
] | 960 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-5, 4, 8, 7],\n [-11, -11, 12, 3],\n [-4, -2, 9, 6],\n [-3, 3, 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"
}
] | 723 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-12, -5, 2, -8],\n [-8, 3, -12, 8],\n [8, -12, 12, 3],\n [8, -2, 1, -11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 404 | MATH |
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