messages listlengths 1 1 | ground_truth stringlengths 1 3 | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "What is the determinant of the matrix:\n[[-10, 7, 2],\n [-9, -5, 3],\n [-1, -4, -4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 469 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-5, -3, -10],\n [0, 6, -10],\n [0, 0, 1]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 970 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[1, 6, 0],\n [0, -3, 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"
}
] | 24 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[4, -8, 5],\n [0, 8, 1],\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"
}
] | 160 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-6, -6, 2],\n [-6, -2, -3],\n [2, -3, -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"
}
] | 302 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[10, 4, 0],\n [0, 10, 4],\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"
}
] | 300 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, 4, -2],\n [4, 1, -3],\n [-2, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 976 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, -9, -3],\n [9, 9, -2],\n [-6, 2, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 92 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 7, -8],\n [-10, 9, -1],\n [-5, -10, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 400 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-6, 1, 10],\n [0, -1, 8],\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"
}
] | 994 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-2, -9, 5],\n [0, -6, 9],\n [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"
}
] | 964 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-9, -2, 7],\n [0, 10, -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"
}
] | 100 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[7, -2, 2],\n [-2, -1, -7],\n [2, -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"
}
] | 783 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[6, -5, -3],\n [-5, -2, 2],\n [-3, 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"
}
] | 869 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, 3, -9],\n [0, 8, -10],\n [0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 280 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-1, 4, 3],\n [0, 6, 7],\n [9, 6, 8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 84 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, -1, -1],\n [-1, -2, 6],\n [-1, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 641 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, -8, -2],\n [-8, 8, -2],\n [-2, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 740 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[1, 4, -9],\n [0, -4, 0],\n [0, 0, 1]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 996 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, 10, 1],\n [9, 6, 3],\n [4, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 240 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[7, -2, 4],\n [-2, 1, 0],\n [4, 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"
}
] | 957 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, -9, -1],\n [0, 5, -5],\n [0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 975 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[3, 5, 9],\n [-3, 6, 6],\n [4, -6, -8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 910 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, -2, -2],\n [-2, 10, -2],\n [-2, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 994 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 0, -3],\n [-4, -2, 5],\n [-8, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 316 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, -10, 6],\n [0, 4, 5],\n [0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 968 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-9, -3, 9],\n [4, 3, 9],\n [-3, -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"
}
] | 808 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, -6, -9],\n [0, -8, -9],\n [0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 480 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[5, -9, -5],\n [1, 1, -7],\n [2, 5, -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"
}
] | 188 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, 2, -10],\n [10, -5, 4],\n [-6, -6, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 651 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[9, -8, -4],\n [-8, 8, 0],\n [-4, 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"
}
] | 888 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, -5, 6],\n [-1, -2, -9],\n [6, -6, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 156 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[0, 3, -4],\n [-4, 0, -5],\n [5, 1, -6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 869 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-10, -1, -8],\n [-1, -9, -2],\n [-8, -2, 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"
}
] | 29 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, -6, 0],\n [-6, 3, -2],\n [0, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 897 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-2, -8, -6],\n [4, 8, -3],\n [-6, 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"
}
] | 330 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, -4, 8],\n [-4, -4, -6],\n [8, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 832 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-6, 2, -3],\n [-1, 9, 9],\n [5, -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"
}
] | 851 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-3, -3, -6],\n [0, -2, 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"
}
] | 994 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-9, 0, 8],\n [0, 1, -2],\n [8, -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"
}
] | 62 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[10, 5, 4],\n [5, -4, 7],\n [4, 7, -1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 919 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, -7, -7],\n [0, -5, 6],\n [-1, -9, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 239 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, -6, 0],\n [-6, 7, -2],\n [0, -2, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 381 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-9, -1, -1],\n [-6, 5, -5],\n [-10, -3, -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"
}
] | 476 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 4, -7],\n [-1, -10, -7],\n [3, -7, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 567 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[5, 10, 3],\n [0, -10, -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"
}
] | 550 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[6, 0, -5],\n [0, -4, 3],\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"
}
] | 192 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, -8, -6],\n [2, -1, -9],\n [4, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 612 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-6, -4, -1],\n [-4, -1, -2],\n [-1, -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"
}
] | 909 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-8, 2, 7],\n [-3, -10, -8],\n [7, -4, 2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 890 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-6, 8, 5],\n [0, -7, 4],\n [0, 0, -7]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 706 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, -3, -2],\n [5, 7, -5],\n [8, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 245 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, 9, 1],\n [-5, -3, 7],\n [6, -2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 84 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-10, 2, 1],\n [5, 5, -2],\n [-9, -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"
}
] | 771 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[5, 3, 2],\n [0, 6, 10],\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"
}
] | 760 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 3, 10],\n [3, 9, -8],\n [3, 7, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 501 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[3, -9, 2],\n [-3, 0, -5],\n [-7, 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"
}
] | 532 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 5, 1],\n [1, 4, 3],\n [1, -2, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 264 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, -7, 4],\n [0, -2, -3],\n [0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 960 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[9, 4, 7],\n [4, -8, -2],\n [7, -2, -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"
}
] | 508 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[2, -2, 3],\n [-2, 2, -2],\n [3, -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"
}
] | 998 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-9, 1, -4],\n [0, -5, 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"
}
] | 550 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-5, 0, 7],\n [0, 1, 6],\n [7, 6, -8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 171 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[9, 1, -4],\n [1, -6, -2],\n [-4, -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"
}
] | 351 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-2, -2, -8],\n [0, 4, 10],\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"
}
] | 64 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-3, -1, -1],\n [4, 0, 7],\n [4, 10, 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"
}
] | 174 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, -10, -9],\n [0, -2, 8],\n [0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-8, -1, 10],\n [0, -8, -3],\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"
}
] | 640 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, 0, -1],\n [-10, 2, 5],\n [10, -9, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 814 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-9, 3, 4],\n [3, -10, -8],\n [4, -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"
}
] | 301 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[3, -1, 6],\n [0, -2, -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"
}
] | 24 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-5, 6, 8],\n [0, 2, -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"
}
] | 940 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, -9, -8],\n [-4, -1, -6],\n [5, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 532 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-10, 2, 7],\n [6, 4, 1],\n [9, 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"
}
] | 650 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[5, -4, 9],\n [0, -8, -7],\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"
}
] | 320 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[1, 4, -5],\n [-3, 10, 9],\n [9, -10, -8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 538 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, -4, 0],\n [-4, -8, -4],\n [0, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 112 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[4, -4, -1],\n [0, -9, -2],\n [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"
}
] | 216 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[6, 2, -2],\n [2, 6, -4],\n [-2, -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"
}
] | 720 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[3, -5, 2],\n [10, 3, 10],\n [7, 8, -8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 56 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-9, 3, 10],\n [-8, 10, 2],\n [8, -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"
}
] | 628 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-9, 4, -6],\n [0, -3, -9],\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"
}
] | 811 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, 8, 1],\n [-3, 0, -8],\n [1, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 984 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, -10, 6],\n [-10, 3, 6],\n [6, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 88 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-5, -10, 5],\n [0, 4, -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"
}
] | 900 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, 0, 2],\n [0, 6, -2],\n [2, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-6, 0, 0],\n [0, -6, -2],\n [0, -2, 3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 132 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, 9, 10],\n [9, 4, -5],\n [10, -5, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 106 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, -9, 10],\n [0, 7, 2],\n [0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 126 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[1, -3, -2],\n [0, -10, 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"
}
] | 970 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, 0, 7],\n [8, 7, 10],\n [-9, -2, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 590 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, 4, 8],\n [0, 5, -6],\n [-2, 10, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 368 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, 2, 2],\n [0, 6, 6],\n [0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 856 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-3, 1, 9],\n [0, 5, 2],\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"
}
] | 910 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[9, 9, -6],\n [-9, 10, -4],\n [-8, 4, -4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 484 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-5, 10, 7],\n [0, 4, -10],\n [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"
}
] | 880 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[2, -9, 2],\n [0, -3, -8],\n [0, 0, 7]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 958 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, 2, -2],\n [0, 9, -9],\n [0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 856 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 1, 1],\n [0, 9, 6],\n [-5, -7, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 679 | 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, -4, 6],\n [-4, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 944 | MATH |
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