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, -6],\n [-6, 9, -2],\n [-6, -2, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 986 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-10, 6, 7],\n [0, -4, -2],\n [0, 0, 8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 320 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-8, -10, 8],\n [0, -3, -7],\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"
}
] | 24 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, 3, -2],\n [3, 1, 4],\n [-2, 4, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 804 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[1, -1, 3],\n [-1, -3, 4],\n [3, 4, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 959 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-5, -2, 0],\n [-2, -8, 4],\n [0, 4, -7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 828 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[7, 10, 9],\n [0, 3, 5],\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"
}
] | 105 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, 8, 4],\n [8, 9, -5],\n [4, -5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 536 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, -3, 9],\n [1, -9, 6],\n [-3, -10, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 937 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-10, -1, 9],\n [0, -4, 9],\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"
}
] | 760 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[6, 4, -6],\n [8, 4, 10],\n [2, 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"
}
] | 320 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[10, 7, -5],\n [-9, 10, 4],\n [-4, -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"
}
] | 823 | 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 [-6, -10, -2],\n [-1, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 34 | 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, -9, 3],\n [2, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 532 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[10, 0, 7],\n [-9, 6, -5],\n [1, -2, 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"
}
] | 44 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, 0, -9],\n [-5, 0, -2],\n [9, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 116 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, 4, 0],\n [4, -9, -3],\n [0, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 380 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-4, -4, -6],\n [-4, -6, 7],\n [-6, 7, -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"
}
] | 708 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[7, -9, 0],\n [4, 1, -4],\n [10, 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"
}
] | 315 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, 3, -2],\n [3, -8, -7],\n [-2, -7, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 547 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-8, 8, -9],\n [0, 3, 3],\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"
}
] | 240 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[10, -5, 3],\n [0, 7, 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"
}
] | 790 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, -8, -4],\n [-8, -5, -10],\n [-4, -10, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 840 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-8, -4, 2],\n [0, -10, -8],\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"
}
] | 480 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 8, -9],\n [-9, 1, -1],\n [5, 6, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 799 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[4, 2, -4],\n [2, -9, 1],\n [-4, 1, 8]]? 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": "Determine the value of det(A) where A =\n[[3, 4, 9],\n [0, 10, -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"
}
] | 180 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[0, -5, 9],\n [4, -2, 9],\n [9, -10, 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"
}
] | 537 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-9, 9, -7],\n [-10, 10, -2],\n [10, 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"
}
] | 780 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-7, -8, 4],\n [0, -4, 10],\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"
}
] | 140 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, -1, -10],\n [0, -6, -4],\n [0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 108 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[4, -2, -2],\n [-2, 7, -8],\n [-2, -8, 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"
}
] | 652 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, 2, 4],\n [2, 6, 0],\n [4, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 824 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[3, -4, 8],\n [0, 4, 10],\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"
}
] | 48 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-8, -1, -6],\n [-1, -5, -2],\n [-6, -2, 3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 305 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-5, -3, -3],\n [1, -5, -4],\n [-5, 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"
}
] | 681 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-9, 8, 5],\n [8, -6, 2],\n [5, 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"
}
] | 426 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[4, 2, 0],\n [2, 1, 6],\n [0, 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"
}
] | 856 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, 0, 9],\n [0, -1, 2],\n [9, 2, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 193 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, -8, 0],\n [-8, -3, 0],\n [0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 440 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[5, 0, 1],\n [5, 2, 2],\n [9, -6, 0]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12 | 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, 7, -9],\n [0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 84 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-4, -7, -2],\n [0, -9, 3],\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"
}
] | 144 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[5, 0, -8],\n [0, 10, -2],\n [-8, -2, 6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 640 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, 6, 5],\n [0, 5, 3],\n [0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 25 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-8, 6, 1],\n [0, 4, 8],\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"
}
] | 320 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-3, 3, 1],\n [-5, -3, 4],\n [-2, -7, -5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 801 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[3, 0, -2],\n [0, 10, 8],\n [-2, 8, 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"
}
] | 948 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-6, 3, -5],\n [0, 7, 10],\n [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"
}
] | 874 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[1, 0, -4],\n [0, -4, 4],\n [-4, 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"
}
] | 44 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[6, -5, -7],\n [1, -6, 10],\n [-9, -9, -5]]\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": "What is the determinant of the matrix:\n[[0, -2, 0],\n [-2, -1, 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"
}
] | 972 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, -9, 5],\n [0, 10, -5],\n [0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 700 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[4, 8, -9],\n [-4, -10, -3],\n [10, 9, -7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 348 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, -7, 9],\n [0, 10, -3],\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[[7, -4, 9],\n [0, -4, 2],\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"
}
] | 860 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 7, -3],\n [7, 0, -2],\n [-3, -2, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 505 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-9, -9, -5],\n [0, -1, -10],\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"
}
] | 9 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-4, -4, -9],\n [0, -7, -7],\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"
}
] | 832 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[4, -6, 6],\n [-6, -8, -2],\n [6, -2, -6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 824 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, 6, 5],\n [6, 10, -2],\n [5, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 358 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, -4, -6],\n [5, 7, 8],\n [-1, 1, 8]]\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[[2, 1, 4],\n [0, 4, 2],\n [0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 80 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[8, 10, 4],\n [0, -9, 0],\n [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"
}
] | 288 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[1, -10, 4],\n [6, 8, 2],\n [-9, 9, 8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 210 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[10, 5, -5],\n [0, -6, 2],\n [0, 0, 2]]? 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": "Determine the value of det(A) where A =\n[[-4, -3, -1],\n [10, -4, -7],\n [-5, 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"
}
] | 291 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, 6, -2],\n [6, 1, 2],\n [-2, 2, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 244 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-5, 5, -3],\n [0, -3, -4],\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"
}
] | 865 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-4, 0, 7],\n [6, -3, 3],\n [-4, 7, -3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 258 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[3, 2, 4],\n [-3, 9, -1],\n [9, 7, -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"
}
] | 562 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, 3, -1],\n [7, 1, -4],\n [9, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 967 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[5, 7, 2],\n [0, 2, 10],\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"
}
] | 90 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-1, -4, -4],\n [-4, 5, -5],\n [-4, -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"
}
] | 596 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-8, 5, 6],\n [-8, -5, -2],\n [3, -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"
}
] | 68 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-9, -10, 3],\n [10, -4, 9],\n [-6, 7, -10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 885 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[7, 1, 1],\n [0, -7, -2],\n [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"
}
] | 147 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, 6, -1],\n [1, -9, 2],\n [-10, -9, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 30 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[6, 9, -7],\n [0, 5, 6],\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"
}
] | 940 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, -7, 5],\n [9, 6, 8],\n [4, 5, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 364 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, 4, -2],\n [4, 5, 0],\n [-2, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 981 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-1, 2, -9],\n [2, 2, 2],\n [-9, 2, -5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 800 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-3, 0, 0],\n [0, 7, -2],\n [0, -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"
}
] | 991 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-3, 2, -2],\n [-10, 9, 4],\n [10, -7, -4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 64 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-7, -4, 2],\n [-4, -6, -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"
}
] | 476 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-9, 3, 3],\n [3, 10, 4],\n [3, 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"
}
] | 324 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, 1, -9],\n [0, 7, -4],\n [9, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 421 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, 6, 0],\n [6, -9, 6],\n [0, 6, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, 1, -4],\n [6, -7, -1],\n [7, -7, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 26 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, 1, -2],\n [-10, 8, 6],\n [-1, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 882 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, -2, -8],\n [0, 2, -10],\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, 3, 6],\n [-1, -9, 10],\n [7, 6, 3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 996 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, 5, 6],\n [0, 2, 7],\n [0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 920 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-9, 2, 0],\n [2, 5, -4],\n [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"
}
] | 752 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[0, 3, -5],\n [-7, -1, -8],\n [-10, -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"
}
] | 3 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-4, 0, 4],\n [0, 7, 2],\n [4, 2, 5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 764 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[8, 7, -1],\n [-7, 5, 4],\n [5, 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"
}
] | 76 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[6, -4, 6],\n [6, -6, 1],\n [1, -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"
}
] | 62 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[0, -9, 5],\n [-6, 10, 7],\n [3, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 679 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-4, -3, 0],\n [2, -2, -2],\n [-6, -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"
}
] | 112 | MATH |
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