messages listlengths 1 1 | ground_truth stringclasses 989
values | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Compute |A| for the matrix A =\n[[1, 6, 10],\n [0, 1, 8],\n [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"
}
] | 992 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[3, 4, -1],\n [0, 8, -9],\n [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"
}
] | 216 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 3, -7],\n [0, -7, -9],\n [0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 720 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[6, 10, 2],\n [10, -4, 8],\n [2, -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"
}
] | 448 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, 10, -6],\n [0, 0, 4],\n [-3, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 800 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[5, 6, -9],\n [-8, -1, -3],\n [-1, -10, -8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 813 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-8, -7, 6],\n [0, -3, 0],\n [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"
}
] | 24 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, 1, -9],\n [6, 6, 4],\n [0, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 904 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[7, -4, 1],\n [-4, 10, 2],\n [1, 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"
}
] | 514 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-6, -5, -2],\n [-5, 0, 0],\n [-2, 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"
}
] | 75 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-10, -6, -1],\n [0, -6, 1],\n [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"
}
] | 400 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-9, -4, 0],\n [0, -9, -8],\n [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"
}
] | 190 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, 2, 2],\n [2, 6, -4],\n [2, -4, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 212 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-9, -6, 0],\n [-6, -5, 0],\n [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"
}
] | 937 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, 1, 6],\n [1, 5, 2],\n [6, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 884 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[0, -4, 2],\n [-4, -8, 0],\n [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"
}
] | 144 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[4, -1, -4],\n [-1, -8, -2],\n [-4, -2, -1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 129 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, 4, -2],\n [4, -10, -3],\n [-2, -3, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 928 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-3, 7, -6],\n [0, -4, -5],\n [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"
}
] | 880 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, 7, 0],\n [-7, 1, -6],\n [-1, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 164 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[4, 10, -2],\n [4, 4, 9],\n [-8, 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"
}
] | 960 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, -7, 3],\n [0, -5, 6],\n [0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 500 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-2, 1, 2],\n [6, -5, 5],\n [10, -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"
}
] | 944 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, 0, 0],\n [0, 5, -3],\n [0, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 238 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-5, -5, -6],\n [-5, 7, -3],\n [-6, -3, -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"
}
] | 93 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, 8, -10],\n [9, -5, -10],\n [-3, 8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 682 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, 0, 6],\n [0, -8, -5],\n [6, -5, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 997 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, 2, -10],\n [6, 1, 3],\n [8, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 696 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[0, -5, 1],\n [-5, 8, 3],\n [1, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 887 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-5, 7, -10],\n [0, -3, 1],\n [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"
}
] | 985 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-1, -4, -3],\n [-7, -7, 5],\n [-2, 1, 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"
}
] | 108 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, -4, 1],\n [2, -10, 4],\n [8, -1, 0]]\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[[5, -8, -2],\n [0, -8, -5],\n [0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 280 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[6, 4, 2],\n [0, 7, -5],\n [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"
}
] | 916 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[7, 0, -3],\n [0, 9, 8],\n [-3, 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"
}
] | 30 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[6, 10, 9],\n [10, -7, -3],\n [9, -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"
}
] | 553 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, 3, 7],\n [0, 1, 6],\n [0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 980 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[10, 0, -6],\n [1, -4, -2],\n [7, 5, 3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 782 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-6, 1, -9],\n [2, 2, -6],\n [2, 5, -8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 866 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[5, -9, 3],\n [0, -8, 9],\n [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"
}
] | 800 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-6, 8, -6],\n [0, -2, -1],\n [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"
}
] | 48 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[0, -7, -9],\n [-9, 9, -7],\n [-9, 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"
}
] | 676 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, -5, 0],\n [-5, 2, 3],\n [0, 3, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 267 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, -6, 1],\n [-6, 0, -3],\n [1, -3, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 378 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, -2, 6],\n [-2, 4, -1],\n [6, -1, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 724 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, -4, -5],\n [-6, -3, 4],\n [-10, -7, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 206 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, -2, -4],\n [-2, 9, -6],\n [-4, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 868 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-4, -3, -4],\n [-10, -2, 10],\n [-10, 4, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 744 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[0, -6, 0],\n [-6, -8, 1],\n [0, 1, -4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 144 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, -6, 1],\n [0, -1, 3],\n [0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 990 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, -1, 7],\n [-1, -8, 4],\n [7, 4, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 962 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[4, 1, -2],\n [-6, -10, -4],\n [-7, -4, 0]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 56 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-3, 6, -3],\n [6, 7, -6],\n [-3, -6, 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"
}
] | 204 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, 4, -4],\n [-1, 9, -6],\n [4, -2, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 762 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, -1, 2],\n [-1, -9, 2],\n [2, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 361 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, -1, -7],\n [0, -6, -2],\n [0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 676 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-5, -4, 4],\n [-4, 2, -9],\n [4, -9, 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"
}
] | 531 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, 0, -3],\n [0, -10, -8],\n [-3, -8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 346 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, -1, 4],\n [0, -5, 9],\n [0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 980 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[3, 5, 4],\n [-4, 8, -8],\n [10, -3, -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"
}
] | 904 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-7, -6, 2],\n [-6, 6, 0],\n [2, 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"
}
] | 366 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[10, 1, -7],\n [-10, 3, -1],\n [8, -7, 7]]? 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": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, 9, 0],\n [0, -2, 7],\n [0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 24 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-5, -4, -2],\n [-4, 3, 0],\n [-2, 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"
}
] | 174 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, 6, -7],\n [-8, 4, 1],\n [-7, -9, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 747 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[10, 1, -10],\n [-10, -4, 9],\n [9, -2, 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"
}
] | 401 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[10, -6, -7],\n [-6, 3, -5],\n [-7, -5, -9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 237 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, -4, 2],\n [0, -7, -6],\n [0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 825 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-7, 4, -2],\n [-5, -10, -1],\n [6, -10, -4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 466 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[10, 5, -4],\n [-8, 5, -6],\n [-9, 7, 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"
}
] | 454 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[5, -8, 1],\n [2, 10, 8],\n [-2, -9, 3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 688 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-3, -2, -8],\n [-2, -7, -2],\n [-8, -2, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 515 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[1, 6, 7],\n [0, 5, -3],\n [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"
}
] | 5 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[3, -1, -6],\n [0, -6, -4],\n [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"
}
] | 180 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-2, 10, 2],\n [7, -2, -9],\n [-2, -1, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 912 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[6, -7, -10],\n [-7, 5, -6],\n [-9, 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"
}
] | 327 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, 3, 2],\n [10, -7, 5],\n [9, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 213 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[2, -1, 1],\n [-10, -8, 9],\n [-3, 3, -1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 945 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, -10, -10],\n [2, -10, -1],\n [4, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 496 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[6, -4, 2],\n [-4, -5, -6],\n [2, -6, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 716 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-9, 2, -6],\n [2, -7, 4],\n [-3, 3, -6]]\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[[3, -8, 9],\n [0, 2, 8],\n [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"
}
] | 970 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, -3, 6],\n [4, -6, -9],\n [0, -5, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 730 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, 6, -10],\n [0, -2, -2],\n [0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 984 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, 2, 5],\n [0, 7, -2],\n [0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 979 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, 2, -3],\n [2, 1, -2],\n [-3, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 999 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, 4, 3],\n [4, -7, -3],\n [3, -3, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 993 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-1, -1, -10],\n [0, 5, 7],\n [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"
}
] | 45 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-1, -6, -7],\n [5, 6, 2],\n [-2, -9, -3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 165 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, -4, 0],\n [-4, 7, 2],\n [0, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 38 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[3, -8, -1],\n [10, 7, 1],\n [-8, 5, 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"
}
] | 943 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-8, -2, 2],\n [-7, 4, 1],\n [-7, -5, -4]]? Round to the nearest integer, then express your answer modulo 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[[-5, -2, -4],\n [0, 1, -9],\n [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"
}
] | 950 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, -4, -2],\n [-4, -10, -4],\n [-2, -4, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 750 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-2, 10, 0],\n [10, 8, -10],\n [0, -10, 3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 852 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-3, 3, -1],\n [3, 0, -1],\n [-1, -1, 7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 946 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[5, 4, 4],\n [0, 1, 8],\n [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"
}
] | 975 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[7, 0, -4],\n [0, 10, 4],\n [-4, 4, 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"
}
] | 728 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, -9, 5],\n [0, 10, 9],\n [0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 350 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-8, -5, -3],\n [0, 5, -10],\n [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"
}
] | 80 | MATH |
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