messages listlengths 1 1 | ground_truth stringclasses 989
values | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "What is the determinant of the matrix:\n[[-6, 4, -5],\n [0, -2, 4],\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"
}
] | 48 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, 7, 4],\n [7, -2, 5],\n [4, 5, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 632 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-3, 8, -3],\n [0, -3, 6],\n [0, 0, -5]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 955 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-1, 6, -4],\n [-1, 2, -8],\n [-3, 4, -6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 80 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-3, 10, 5],\n [0, -6, -7],\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"
}
] | 126 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, 8, 6],\n [0, -9, 6],\n [0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 595 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[5, -4, 6],\n [0, 7, 2],\n [0, 0, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 245 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[10, -4, 0],\n [0, 3, 3],\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"
}
] | 90 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-8, 8, -3],\n [0, 4, 4],\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"
}
] | 808 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, -4, -5],\n [-2, 10, -2],\n [-3, -4, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 786 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[9, 2, 10],\n [-7, 3, 8],\n [3, 8, -5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 617 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, 7, 9],\n [-6, -5, -7],\n [-6, 5, 8]]\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[[5, 2, 0],\n [10, -6, -2],\n [-7, -7, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 258 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-10, 6, -3],\n [6, -2, -3],\n [-3, -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"
}
] | 264 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, 2, 0],\n [3, -9, 8],\n [-10, -7, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 677 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-1, 1, -4],\n [1, 7, 4],\n [-4, 4, 10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 792 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, 7, 4],\n [2, 5, -8],\n [3, -10, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 896 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, -2, 8],\n [0, 8, -3],\n [0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 616 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, 5, -2],\n [0, -7, -10],\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[[-6, 3, -2],\n [3, 8, 4],\n [-2, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 731 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[5, -1, 10],\n [0, 3, 0],\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"
}
] | 30 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[3, -3, 10],\n [0, 10, -4],\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"
}
] | 970 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-1, -7, 9],\n [0, -8, 4],\n [0, 0, -5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 960 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, 5, 1],\n [5, 4, 4],\n [1, 4, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 521 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[1, -9, 2],\n [-6, -4, 2],\n [-9, 9, 0]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 964 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[2, 2, 0],\n [2, -1, 6],\n [0, 6, -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"
}
] | 952 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-1, 9, -4],\n [-4, -10, -1],\n [8, -6, -1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 472 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, -7, 4],\n [1, -3, -9],\n [7, 10, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 551 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-1, 3, 1],\n [0, 9, -2],\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"
}
] | 54 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[4, -10, 8],\n [0, 5, 2],\n [0, 0, -7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 860 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-1, 6, -10],\n [-5, 7, -5],\n [-6, 1, 9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-10, -10, 4],\n [-10, 8, -1],\n [-6, 6, 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"
}
] | 572 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-10, -1, 3],\n [0, -3, 3],\n [0, 0, -9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 730 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, 3, 0],\n [3, -9, 0],\n [0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 352 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-1, 2, 3],\n [10, -7, 8],\n [-3, -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"
}
] | 676 | 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 [4, 3, 6],\n [-4, 6, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 526 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-3, -8, 2],\n [-8, 9, 3],\n [2, 3, -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"
}
] | 623 | 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, 6, 5],\n [2, 5, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 451 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-2, -7, 5],\n [0, 9, -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"
}
] | 946 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[6, 2, 2],\n [0, -5, -1],\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"
}
] | 820 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[10, -6, -3],\n [7, 0, 8],\n [3, -3, 0]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 159 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, -10, 0],\n [0, -8, -6],\n [0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 680 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, 9, -9],\n [0, -8, 3],\n [0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 616 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-9, -4, -6],\n [-4, 7, 0],\n [-6, 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"
}
] | 301 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[10, 2, 4],\n [4, -4, 9],\n [8, -5, 2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 546 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, 6, 0],\n [0, 8, -8],\n [0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 288 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[8, 10, -7],\n [-3, -7, 1],\n [10, 5, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 727 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[1, 4, 1],\n [0, -5, -4],\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"
}
] | 5 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 3, 3],\n [3, -10, 4],\n [3, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 156 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, -6, -2],\n [0, -5, 0],\n [0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 920 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-8, -5, 3],\n [-1, 9, 9],\n [-3, -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"
}
] | 94 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-7, 1, 3],\n [0, 6, -9],\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"
}
] | 42 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[9, 2, -4],\n [2, 4, -4],\n [-4, -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"
}
] | 632 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, 3, 0],\n [0, 2, -1],\n [0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 42 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, -3, -4],\n [-3, 10, 6],\n [-4, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 230 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, 2, -3],\n [5, 0, -10],\n [2, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 945 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-9, 4, -4],\n [0, 2, 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"
}
] | 72 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[10, 3, -6],\n [3, 3, 2],\n [-6, 2, 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"
}
] | 948 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, 6, 8],\n [6, 10, -8],\n [8, -8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 320 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-8, -2, 10],\n [8, -7, 9],\n [7, -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"
}
] | 188 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[6, -5, -3],\n [9, 9, -8],\n [1, -8, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 701 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[9, 4, -2],\n [0, 6, -9],\n [0, 0, -7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 622 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[3, -2, -7],\n [-2, 5, -2],\n [-7, -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"
}
] | 599 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[2, -3, -2],\n [0, -9, 4],\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"
}
] | 36 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[3, 0, 9],\n [0, 2, 7],\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"
}
] | 60 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, -5, -3],\n [10, 4, 3],\n [10, 10, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 68 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 7, 4],\n [7, -9, -8],\n [4, -8, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 254 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[0, -10, 7],\n [-10, -7, 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"
}
] | 763 | 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 [3, -5, -10],\n [-8, 3, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 862 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-9, 1, -2],\n [1, -6, 6],\n [-2, 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"
}
] | 801 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-5, 3, 3],\n [3, 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"
}
] | 957 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, 4, -3],\n [6, -5, 8],\n [7, -3, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 939 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, -3, 2],\n [-3, 3, 2],\n [2, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 968 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[5, -8, 9],\n [-9, 5, 4],\n [4, 7, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 797 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, -2, 8],\n [-2, 1, 7],\n [8, 7, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 555 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-6, -6, -6],\n [0, -9, 6],\n [0, 0, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 378 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[1, 0, -5],\n [0, 8, -7],\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"
}
] | 984 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-7, 6, -9],\n [1, -8, -8],\n [-2, -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"
}
] | 225 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, 8, 2],\n [-7, -10, -2],\n [-9, 10, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 616 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-6, -9, 9],\n [0, 8, 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"
}
] | 288 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, -10, -2],\n [0, -3, 5],\n [0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 760 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-10, 2, 3],\n [-8, -7, 8],\n [4, 7, 8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 228 | 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, 4, 4],\n [2, 4, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 955 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-1, -4, -2],\n [-4, -9, -1],\n [-2, -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"
}
] | 49 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[8, -8, 5],\n [0, 9, 0],\n [-9, -4, -1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 333 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, -9, -5],\n [0, 7, 8],\n [0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 804 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, -6, -9],\n [0, 8, 8],\n [0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-10, -1, 4],\n [-1, 8, 5],\n [4, 5, 10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 272 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-5, -8, 0],\n [0, 2, 8],\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"
}
] | 950 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-6, 7, -8],\n [0, 4, -6],\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"
}
] | 192 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[9, 1, -7],\n [-7, 1, -3],\n [-5, -10, 1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 236 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, -2, 6],\n [-2, -3, 5],\n [6, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 860 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 7, 6],\n [-6, -5, -5],\n [-3, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 881 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-2, -5, 8],\n [-1, 8, 1],\n [-3, -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"
}
] | 63 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, 10, 8],\n [-8, -8, 1],\n [7, 8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 854 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 2, 1],\n [0, -5, 0],\n [0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 600 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-7, 3, 5],\n [0, -2, -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"
}
] | 70 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, -10, 1],\n [-3, 0, 2],\n [0, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 157 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[0, 9, 8],\n [3, -6, 8],\n [-8, 10, -2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 334 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[10, -4, 10],\n [-4, -6, -2],\n [10, -2, 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"
}
] | 112 | MATH |
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