messages listlengths 1 1 | ground_truth stringclasses 989
values | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Compute |A| for the matrix A =\n[[7, -10, -6],\n [0, 3, 5],\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"
}
] | 42 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[5, -3, 4],\n [-4, -2, -2],\n [4, -1, 4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 974 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[0, -7, 3],\n [10, 2, -2],\n [4, -9, -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"
}
] | 342 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[5, -10, 0],\n [-10, 1, -7],\n [0, -7, -2]]? 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": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, 5, 6],\n [2, -4, 0],\n [1, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 996 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[7, 10, -8],\n [0, -3, -4],\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"
}
] | 42 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[1, -1, 0],\n [0, -1, 2],\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"
}
] | 991 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[3, -3, 0],\n [-3, -1, -2],\n [0, -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"
}
] | 916 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, 8, -7],\n [-1, 6, 10],\n [0, 7, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 185 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[6, -3, -1],\n [-6, 10, 9],\n [8, 8, 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"
}
] | 900 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, -4, -4],\n [-4, 1, 4],\n [-4, 4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 936 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-9, -4, 4],\n [-5, -5, -10],\n [-1, 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"
}
] | 15 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[5, 8, -2],\n [8, 10, 1],\n [-2, 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"
}
] | 783 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[1, -4, 1],\n [-3, -10, -2],\n [3, 5, -3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 115 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, -4, -8],\n [-4, -10, 1],\n [-8, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 495 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, 4, 0],\n [4, -1, 2],\n [0, 2, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 908 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 0, 2],\n [0, 0, -9],\n [2, -9, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 810 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-1, 5, 2],\n [4, 3, -5],\n [2, -8, -8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 98 | 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 [0, 1, 7],\n [0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 990 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[7, 8, 6],\n [8, 1, -4],\n [6, -4, 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"
}
] | 126 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[3, -10, -4],\n [0, -5, -2],\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"
}
] | 105 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[3, -8, -1],\n [0, -7, -3],\n [5, -6, -5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 136 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, 10, -5],\n [-10, 0, 10],\n [-5, 8, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 560 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, 4, -6],\n [-3, -8, 10],\n [8, 6, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 964 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[1, -5, -4],\n [-5, 3, 3],\n [-4, 3, 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"
}
] | 41 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[4, -8, -7],\n [0, -1, 2],\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"
}
] | 984 | 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 [0, 3, -7],\n [0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-8, -8, -2],\n [-8, -6, 0],\n [-2, 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"
}
] | 864 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[0, -10, -2],\n [10, 10, -6],\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"
}
] | 500 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, 2, 0],\n [2, -2, 8],\n [0, 8, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 924 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[2, 7, -10],\n [3, -7, 10],\n [-1, -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"
}
] | 165 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[3, 0, -3],\n [0, -1, 4],\n [-3, 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"
}
] | 973 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[2, 3, 1],\n [3, 2, 0],\n [1, 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"
}
] | 993 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, -5, 9],\n [6, 6, 7],\n [10, 5, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 605 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[1, 8, 6],\n [0, 9, 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"
}
] | 928 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-10, 10, -9],\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"
}
] | 900 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-2, 1, 5],\n [2, 2, 5],\n [-8, 6, 9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 106 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, -9, -2],\n [-9, -4, 4],\n [-2, 4, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 689 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, -5, -4],\n [-5, 1, 0],\n [-4, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 669 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 8, 9],\n [10, -9, -10],\n [-7, -4, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 25 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[5, 9, -7],\n [0, 10, 3],\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"
}
] | 550 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[3, -6, -1],\n [-10, 9, 9],\n [1, -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"
}
] | 322 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[2, 9, -4],\n [0, 4, 4],\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"
}
] | 960 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[5, 4, -1],\n [0, -5, -3],\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"
}
] | 950 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-9, -2, 10],\n [4, -2, 7],\n [-9, 6, 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"
}
] | 564 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-7, 1, -8],\n [1, 8, 4],\n [6, -8, -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"
}
] | 818 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[1, 2, -4],\n [2, -9, 2],\n [-4, 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"
}
] | 173 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, 2, -7],\n [0, -9, 9],\n [6, 7, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 793 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[0, -5, 9],\n [2, -6, -2],\n [7, -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"
}
] | 370 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, 10, 1],\n [3, 3, -7],\n [3, -7, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 592 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-8, -2, 8],\n [-2, 9, -4],\n [8, -4, -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"
}
] | 60 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[2, -8, 4],\n [0, -8, 3],\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"
}
] | 936 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[5, 1, 3],\n [1, 1, 2],\n [3, 2, 4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 999 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-5, -2, 3],\n [-2, 3, -6],\n [3, -6, 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"
}
] | 35 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[4, 2, 8],\n [2, -1, -1],\n [8, -1, 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"
}
] | 980 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 9, 6],\n [0, -9, 4],\n [0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 324 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, -2, 4],\n [9, 5, 5],\n [-7, -9, 1]]\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[[1, 1, 1],\n [0, -7, -1],\n [0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 930 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, -4, 2],\n [-4, -3, 5],\n [2, 5, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 827 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, -1, 1],\n [-1, -4, -4],\n [1, -4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 956 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, -7, 4],\n [-7, 2, 0],\n [4, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 554 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-8, -9, 3],\n [6, -4, 5],\n [3, -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"
}
] | 581 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-6, 3, -10],\n [0, 3, -4],\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"
}
] | 892 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, 10, -1],\n [0, -4, 5],\n [0, 0, -7]]\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[[-4, 0, -4],\n [0, -8, 4],\n [-4, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 288 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-3, -4, 1],\n [9, -6, 1],\n [-7, -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"
}
] | 338 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, 8, -1],\n [0, -1, -3],\n [0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 980 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, -9, -3],\n [-3, -8, -3],\n [-5, -2, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 459 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-5, -3, 0],\n [-3, -7, -6],\n [0, -6, 8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 388 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, -10, 3],\n [0, -10, -5],\n [0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 800 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[10, 4, 3],\n [4, 2, 3],\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"
}
] | 960 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-8, 3, 1],\n [0, -4, -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"
}
] | 872 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[2, 5, 2],\n [-1, -5, -9],\n [-2, 10, -10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 280 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, -6, 3],\n [-6, 10, -2],\n [3, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 994 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-10, -1, -7],\n [-1, -10, -4],\n [-7, -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"
}
] | 901 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-9, -2, 4],\n [-10, 6, -7],\n [-8, 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"
}
] | 433 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[2, -8, 2],\n [-5, -10, 4],\n [-4, -6, 10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 556 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, -4, -5],\n [0, -7, -7],\n [0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 168 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, 7, 6],\n [-10, -5, 9],\n [-10, -10, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 410 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, 4, -1],\n [0, 5, -1],\n [0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 300 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, -5, -8],\n [0, 1, 6],\n [0, 0, 6]]\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, 4, 4],\n [-3, 8, -4],\n [1, 8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 48 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 2, -2],\n [2, 1, 0],\n [-2, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 884 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, 3, -8],\n [10, 0, 7],\n [-6, 6, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 418 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, -1, -3],\n [8, 2, 10],\n [-9, 5, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[1, 4, -7],\n [0, -3, 1],\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"
}
] | 30 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[4, 8, -2],\n [0, 6, -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"
}
] | 168 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-1, 1, 10],\n [0, -5, 1],\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"
}
] | 980 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, 7, 5],\n [0, -7, 6],\n [0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 958 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, -5, 3],\n [-5, -3, 7],\n [3, 7, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[0, -4, 4],\n [-4, 3, 0],\n [4, 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"
}
] | 888 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-2, -6, -10],\n [-6, -1, -2],\n [7, 8, -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"
}
] | 632 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[9, 2, 3],\n [2, 9, 2],\n [3, 2, -9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 214 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-4, -3, 8],\n [-3, 0, 7],\n [8, 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"
}
] | 806 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[2, 4, -4],\n [0, -5, 5],\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"
}
] | 30 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[6, -10, 9],\n [0, -8, -2],\n [-9, 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"
}
] | 740 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, -2, -5],\n [-2, 5, 2],\n [-5, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 837 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 8, 10],\n [0, 3, -7],\n [0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 240 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-9, 5, -5],\n [0, -8, 5],\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"
}
] | 424 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[1, 10, -10],\n [0, -2, 1],\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"
}
] | 10 | MATH |
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