messages listlengths 1 1 | ground_truth stringclasses 989
values | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Compute |A| for the matrix A =\n[[-3, 9, 8],\n [-6, 8, 8],\n [8, 8, -6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 692 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, -1, -3],\n [0, -4, -8],\n [0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 200 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, -2, 5],\n [0, 2, 0],\n [0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 880 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[0, -1, -4],\n [-1, 1, -6],\n [-4, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 938 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-4, -1, 4],\n [-1, 10, -4],\n [4, -4, -4]]\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": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, 9, -2],\n [3, -6, -3],\n [3, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 120 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-9, -4, 7],\n [0, 9, -8],\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"
}
] | 838 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[5, -9, -6],\n [0, -1, -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"
}
] | 10 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[2, 0, -2],\n [0, -1, 7],\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 |
[
{
"content": "What is the determinant of the matrix:\n[[-4, 6, -4],\n [6, 0, 0],\n [-4, 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"
}
] | 108 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, -4, 0],\n [-4, -3, 4],\n [0, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 122 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, 3, 2],\n [3, -3, 2],\n [2, 2, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 823 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-10, 10, -8],\n [0, -8, 5],\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"
}
] | 360 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[0, -3, 0],\n [-3, 10, -3],\n [4, 1, -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[[-9, 6, -6],\n [0, 10, 9],\n [0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 450 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[10, -6, 3],\n [-6, 10, -6],\n [3, -6, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 638 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, -4, -9],\n [0, 9, 5],\n [0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 216 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[2, 6, -5],\n [0, 4, 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"
}
] | 80 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 6, -8],\n [0, 2, -3],\n [0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 50 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[5, -2, -4],\n [0, -4, 3],\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"
}
] | 880 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-4, 5, 9],\n [6, 8, -4],\n [-2, 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"
}
] | 664 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[0, -9, 5],\n [-3, -4, -6],\n [4, -3, -10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 611 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-5, 8, -6],\n [0, -3, 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"
}
] | 120 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[3, 3, 0],\n [-8, 9, -5],\n [-4, -4, -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"
}
] | 541 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[0, 3, -3],\n [-4, 1, -7],\n [1, 4, 10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 150 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, -9, -8],\n [10, 2, -2],\n [2, -1, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 278 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, 5, 1],\n [0, -6, 9],\n [3, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 99 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-5, -2, -8],\n [0, -8, 7],\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"
}
] | 840 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, 4, 9],\n [-10, 1, 1],\n [9, -2, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 807 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, 1, 2],\n [1, -4, -3],\n [2, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 50 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, 9, 2],\n [-1, -2, -5],\n [-7, 7, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 201 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, 4, -9],\n [-10, 6, -5],\n [-5, -4, 8]]\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[[7, 1, -3],\n [0, -8, 9],\n [0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 440 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-3, 4, 2],\n [8, 7, 10],\n [-9, 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"
}
] | 381 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-10, 2, -2],\n [2, -6, 6],\n [-2, 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"
}
] | 832 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-6, 3, -1],\n [0, 7, -1],\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"
}
] | 126 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-7, 1, -2],\n [1, -3, 4],\n [-2, 4, 5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 208 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-9, 4, 8],\n [4, -5, -6],\n [8, -6, 4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 376 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-5, -5, -3],\n [0, 10, 2],\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"
}
] | 800 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, 0, -9],\n [8, -4, -2],\n [1, 6, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 484 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, 9, -1],\n [8, -5, -6],\n [-6, -1, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 250 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[6, 1, -3],\n [-1, -2, -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"
}
] | 452 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[3, -8, 1],\n [-8, -6, -5],\n [1, -5, 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"
}
] | 191 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, 7, 1],\n [0, 4, -9],\n [4, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-2, 6, 4],\n [6, -7, -4],\n [4, -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"
}
] | 886 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[10, 6, 7],\n [0, -5, 7],\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"
}
] | 800 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, -5, 0],\n [0, -8, 3],\n [0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 568 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[7, 5, -6],\n [-3, -3, -1],\n [-2, -5, -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"
}
] | 939 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[2, 9, 7],\n [0, 10, 9],\n [0, 0, 10]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 200 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, 5, 1],\n [8, 10, -7],\n [4, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 622 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[1, 5, -7],\n [0, -6, -3],\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"
}
] | 36 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, 9, 1],\n [0, -5, 0],\n [0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 820 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-6, -10, 5],\n [-1, -1, 6],\n [4, 5, -1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 939 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[3, -10, 10],\n [0, 5, -3],\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"
}
] | 910 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-7, 1, -9],\n [4, -8, -8],\n [6, -8, 4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 464 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, -10, 9],\n [0, -1, -9],\n [0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 986 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[2, -9, 3],\n [0, 3, -7],\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"
}
] | 964 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[1, 10, -1],\n [0, 4, -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"
}
] | 964 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, -2, -1],\n [0, -7, 2],\n [0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 140 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, 0, 3],\n [-3, -6, 6],\n [8, -10, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 474 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[3, 4, -6],\n [4, -1, 2],\n [-6, 2, 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": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, 6, -3],\n [0, -7, 7],\n [0, 0, 2]]\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[[-9, -10, -5],\n [0, -8, 4],\n [0, 0, -10]]\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[[-7, 8, 4],\n [3, 2, 7],\n [-9, 10, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 292 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, 0, 0],\n [0, 0, -8],\n [0, -8, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 384 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[10, -4, 7],\n [-4, -4, 2],\n [7, 2, -1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 100 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[7, -7, 10],\n [0, 4, 1],\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"
}
] | 972 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[10, -7, -8],\n [-3, -2, 4],\n [-5, 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"
}
] | 122 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[10, 0, 9],\n [-1, -9, 5],\n [-6, 7, -9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 911 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, 3, -3],\n [-9, 4, -3],\n [-4, -5, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 814 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[5, -10, -8],\n [0, -2, -6],\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"
}
] | 990 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-4, -5, -2],\n [0, 5, 9],\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[[10, 5, 0],\n [5, -5, -4],\n [0, -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"
}
] | 765 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-9, 7, 7],\n [0, -8, 3],\n [0, 0, -1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 928 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[2, 1, 8],\n [9, -5, -1],\n [-1, -9, -4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 371 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, -4, -3],\n [1, -6, -1],\n [6, 10, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 946 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, 6, -7],\n [0, -3, -5],\n [0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 54 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[9, 8, 2],\n [8, 3, -2],\n [2, -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"
}
] | 851 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-2, 8, 0],\n [7, 4, -6],\n [-5, -3, 6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 892 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-2, 7, 1],\n [0, 10, -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"
}
] | 940 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[6, -2, 0],\n [-2, 4, 7],\n [0, 7, -5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 606 | 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 [0, -1, 4],\n [0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 976 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-10, 0, -3],\n [0, 8, 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"
}
] | 600 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, 1, 5],\n [0, 8, -2],\n [0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 744 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, -4, -2],\n [-4, -4, -2],\n [-2, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 980 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-4, 6, -5],\n [0, 2, 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"
}
] | 56 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-5, -6, 2],\n [9, 2, 7],\n [1, -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"
}
] | 760 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[5, -4, -3],\n [0, 9, -9],\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"
}
] | 640 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, 5, -2],\n [-5, -9, 7],\n [-2, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 945 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, -10, 6],\n [4, -1, -7],\n [-4, -7, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 458 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, 1, 3],\n [0, -1, -8],\n [0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 72 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[3, 2, 8],\n [2, 5, -5],\n [8, -5, 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"
}
] | 511 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, 9, 2],\n [0, -10, 4],\n [0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 50 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-4, 1, -6],\n [1, 7, 8],\n [-6, 8, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 792 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[9, -2, 10],\n [0, -7, -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"
}
] | 496 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, -5, -4],\n [0, 3, -1],\n [0, 0, 10]]\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[[-3, 2, 2],\n [2, 10, 8],\n [2, 8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 352 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[10, -4, 6],\n [0, -9, 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"
}
] | 460 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-4, -3, 2],\n [0, 2, -5],\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"
}
] | 936 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-10, -3, -6],\n [-4, -10, -1],\n [-8, 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"
}
] | 540 | MATH |
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