messages listlengths 1 1 | ground_truth stringclasses 989
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[[1, -6, -4],\n [-6, -9, -3],\n [-4, -3, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 306 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, 7, -4],\n [4, -3, 1],\n [5, -7, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-6, -10, 1],\n [0, -8, -8],\n [-5, -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"
}
] | 512 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[2, -3, -6],\n [-3, -3, -1],\n [-6, -1, 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"
}
] | 25 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[5, 6, 2],\n [6, -10, -2],\n [2, -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"
}
] | 144 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[6, 10, -3],\n [0, 10, -8],\n [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": "Determine the value of det(A) where A =\n[[-8, 0, 9],\n [7, 9, -3],\n [6, 10, -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"
}
] | 336 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[7, 3, -4],\n [3, 9, 0],\n [-4, 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"
}
] | 342 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, -4, -4],\n [-4, 3, 4],\n [-4, 4, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 948 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, -6, -7],\n [-6, 0, -2],\n [-7, -2, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 464 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[2, -7, -9],\n [0, 3, 5],\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"
}
] | 6 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-9, -8, -4],\n [-8, 3, -1],\n [-4, -1, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 79 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 6, 3],\n [3, 3, 9],\n [-1, 9, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 594 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-10, 10, -4],\n [-4, 0, 3],\n [-7, -1, -10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 344 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, -2, 1],\n [-2, 1, -8],\n [1, -8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 967 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 0, 6],\n [0, -2, -1],\n [6, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 107 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, 3, -2],\n [0, -9, 10],\n [0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 271 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[10, 0, 1],\n [-7, -2, 0],\n [4, -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"
}
] | 938 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[4, -6, -6],\n [-6, -9, -5],\n [-6, -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"
}
] | 440 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, -1, 1],\n [0, -9, -1],\n [0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 648 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[10, 4, -10],\n [0, 8, -4],\n [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"
}
] | 600 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 0, -3],\n [3, -9, 0],\n [-5, 9, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 694 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[8, -2, 4],\n [-2, -6, 5],\n [4, 5, -8]]\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": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, -10, -1],\n [0, 1, 4],\n [0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, 7, 9],\n [0, -2, 5],\n [0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 972 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-9, 3, -1],\n [0, 7, 0],\n [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"
}
] | 559 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[10, 0, -2],\n [4, 3, -5],\n [-5, -6, 0]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 718 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-3, -5, -3],\n [9, 7, -1],\n [-6, 7, -2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 586 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[5, 3, -7],\n [0, -4, -5],\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"
}
] | 20 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[1, 1, -3],\n [0, -6, 1],\n [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"
}
] | 982 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, 2, 2],\n [2, 2, 0],\n [2, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 848 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[3, -2, -8],\n [-2, 10, -8],\n [-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"
}
] | 730 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[8, -5, -6],\n [-5, -6, 6],\n [-6, 6, -10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 18 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, -6, -4],\n [-6, -8, -2],\n [-4, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 980 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-10, 3, 0],\n [3, 10, -4],\n [0, -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"
}
] | 596 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[3, 6, 7],\n [0, -8, 4],\n [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"
}
] | 192 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, -1, -8],\n [0, -3, -9],\n [1, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 907 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[3, -4, -4],\n [8, 1, -5],\n [10, 10, 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"
}
] | 210 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, -4, -4],\n [-4, 9, -4],\n [-4, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 670 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, 10, -7],\n [-1, 0, -3],\n [10, 5, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 590 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[0, -2, 5],\n [-2, 8, 0],\n [5, 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"
}
] | 784 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[2, 3, 10],\n [9, 2, 2],\n [-6, -1, 9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 791 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, 6, 8],\n [10, -10, 8],\n [-4, -9, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 194 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-3, 2, 0],\n [2, 4, 0],\n [0, 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"
}
] | 64 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[6, 3, 4],\n [3, -10, -1],\n [4, -1, -6]]? Round to the nearest integer, then express your answer 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[[-7, 2, 9],\n [2, 4, 4],\n [9, 4, -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"
}
] | 28 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, -1, 2],\n [9, -4, -3],\n [6, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 46 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-5, 6, -4],\n [6, -9, -4],\n [-4, -4, 10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 506 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-9, -3, 6],\n [-3, 10, -2],\n [6, -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"
}
] | 857 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, 8, 4],\n [-3, -6, 9],\n [-5, 8, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 456 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-1, 9, -8],\n [0, 6, -7],\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"
}
] | 940 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, 9, -2],\n [0, -6, 8],\n [0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 982 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[6, 7, -8],\n [0, 8, -3],\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"
}
] | 568 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-1, -4, 10],\n [0, -5, 9],\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"
}
] | 35 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, -9, 4],\n [0, 9, 7],\n [0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 45 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, -5, 0],\n [-5, -1, 4],\n [0, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 160 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, 0, 0],\n [0, 8, 0],\n [0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 32 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, 9, -8],\n [2, 4, -6],\n [3, -10, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 642 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, 7, 3],\n [0, -10, -9],\n [0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 820 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-8, -4, 6],\n [4, -9, -6],\n [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"
}
] | 158 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[7, -5, 0],\n [-5, -1, 4],\n [0, 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"
}
] | 80 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 0, 5],\n [-4, 8, 1],\n [6, 6, 9]]\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[[-8, 6, -4],\n [0, 10, -10],\n [0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 560 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[9, -9, 2],\n [0, -9, 4],\n [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"
}
] | 729 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-6, 6, 10],\n [6, -3, 1],\n [10, 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"
}
] | 372 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, 10, 1],\n [0, -3, -3],\n [0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 15 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-3, 8, 1],\n [0, -2, 0],\n [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"
}
] | 36 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[9, 3, -8],\n [-2, -9, 10],\n [6, 5, -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"
}
] | 53 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[6, -4, 3],\n [0, 6, -8],\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"
}
] | 964 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[10, 4, 1],\n [8, -5, 10],\n [8, 7, 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"
}
] | 552 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[8, -2, -8],\n [2, -6, -6],\n [2, 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"
}
] | 884 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-7, 4, -7],\n [0, 5, 4],\n [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"
}
] | 825 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[6, 7, -1],\n [0, -3, 6],\n [0, 0, -6]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 108 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, -9, 8],\n [0, 10, 1],\n [0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 940 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[3, -6, -10],\n [0, -9, 6],\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"
}
] | 730 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[3, -8, -4],\n [1, 1, 3],\n [8, 1, 6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 893 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 0, -4],\n [0, -4, 3],\n [-4, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 394 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, -6, -8],\n [-6, -7, 6],\n [-8, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 224 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-8, 4, -6],\n [4, 2, -8],\n [-6, -8, -10]]\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[[-1, -1, -1],\n [-1, 6, 0],\n [-1, 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"
}
] | 50 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, -1, -5],\n [0, 4, 10],\n [0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 800 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, -1, 0],\n [0, 2, 8],\n [0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[5, 3, 5],\n [3, 5, -2],\n [5, -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"
}
] | 667 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, 3, -3],\n [-9, -2, -4],\n [-9, 2, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 486 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, -2, -6],\n [0, 4, 5],\n [0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 904 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, 7, 8],\n [7, -8, -3],\n [8, -3, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 183 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[3, 7, -10],\n [0, 5, -6],\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"
}
] | 940 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[8, -10, 4],\n [6, -9, 8],\n [0, 6, 7]]\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": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, -5, 9],\n [0, -10, -4],\n [0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 440 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-8, 2, 9],\n [-3, -2, -7],\n [-6, -3, -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"
}
] | 159 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-9, 6, -4],\n [0, -1, 8],\n [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"
}
] | 27 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, 4, 0],\n [0, -8, -10],\n [0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 384 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[6, 7, 5],\n [-5, 3, -4],\n [-6, 1, -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"
}
] | 151 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-1, 6, -1],\n [0, 5, 7],\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": "Compute |A| for the matrix A =\n[[1, 1, 2],\n [0, -7, 9],\n [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"
}
] | 14 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, 0, -6],\n [0, 6, 10],\n [0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 252 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-4, 1, 1],\n [0, -1, 0],\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"
}
] | 8 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, -3, 9],\n [0, 6, -4],\n [0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 270 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[0, 0, 1],\n [0, 8, -7],\n [1, -7, 6]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 992 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, 2, 6],\n [0, 1, 2],\n [0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 72 | MATH |
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