messages listlengths 1 1 | ground_truth stringclasses 992
values | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, -12, -7, 4],\n [0, 5, -2, 10],\n [0, 0, -9, 1],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 425 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[4, 6, 1, 2],\n [6, 7, -6, 8],\n [1, -6, 11, -1],\n [2, 8, -1, 12]]\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"
}
] | 972 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 0, 4, 2],\n [0, -3, -11, -1],\n [4, -11, 9, -2],\n [2, -1, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 248 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-8, 8, -8, 11],\n [0, 4, 12, 10],\n [0, 0, -11, -4],\n [0, 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"
}
] | 408 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[5, 1, 8, -6],\n [-9, 12, 11, 0],\n [-3, 12, -5, 2],\n [2, 5, -6, 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"
}
] | 158 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, -7, 9, -12],\n [-7, -2, -10, 3],\n [9, -10, 2, 8],\n [-12, 3, 8, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 589 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, -3, 12, -4],\n [0, 11, 0, -7],\n [0, 0, -7, 7],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 224 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, -9, 2, -2],\n [0, -2, 2, -2],\n [0, 0, -3, 1],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 820 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, -9, 6, -9],\n [7, -1, 1, 5],\n [7, 0, -4, -2],\n [-7, 0, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-9, -8, -8, 8],\n [-8, 0, 0, -8],\n [-8, 0, 8, 0],\n [8, -8, 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"
}
] | 872 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[3, -7, -4, 8],\n [-2, -3, 4, -12],\n [-1, -9, -3, -2],\n [-4, 4, 10, 5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 849 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, -8, 12, -8],\n [0, 6, -10, -7],\n [0, 0, -6, 11],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 864 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-3, 8, 0, -1],\n [-1, 10, -5, 11],\n [5, 5, 6, 2],\n [9, -8, 5, -6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 927 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, -8, -4, -9],\n [-5, 7, 6, -3],\n [10, -1, -10, 5],\n [-7, 1, -8, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 198 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, -1, 12, 8],\n [0, 7, 12, 12],\n [0, 0, 5, -3],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 825 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, 6, 4, -5],\n [0, 7, -1, 3],\n [0, 0, 5, -11],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 310 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[9, -10, 3, -11],\n [-10, 8, -10, -4],\n [-10, -7, -10, -11],\n [2, 5, -12, 1]]? 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": "Compute |A| for the matrix A =\n[[-3, -7, -6, 7],\n [-3, -9, -4, 9],\n [3, -4, 8, -6],\n [9, 0, -5, 0]]\nRound to the nearest integer, then take the result 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[[1, -6, 9, -12],\n [-6, 12, -3, -6],\n [9, -3, 9, -8],\n [-12, -6, -8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 144 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-9, -3, 9, 8],\n [0, 4, -7, 8],\n [0, 0, 9, 5],\n [0, 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"
}
] | 620 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, 8, 0, 2],\n [8, -10, -11, -7],\n [0, -11, -10, -1],\n [2, -7, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 598 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[5, -2, -3, 6],\n [-5, 8, 3, 4],\n [0, -6, 4, -10],\n [-2, -11, -7, 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"
}
] | 488 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, -2, -4, -1],\n [-2, -3, -8, -8],\n [-4, -8, 9, -2],\n [-1, -8, -2, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 181 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-2, 6, -5, -3],\n [-4, -4, -12, 1],\n [-4, -10, 8, 4],\n [12, 1, 2, 11]]\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"
}
] | 492 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[4, 7, 0, 1],\n [7, 7, 7, -3],\n [0, 7, 12, -4],\n [1, -3, -4, 11]]\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"
}
] | 501 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, 4, -4, 0],\n [4, 9, -2, 10],\n [-4, -2, -9, -4],\n [0, 10, -4, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 660 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, 1, 0, 4],\n [1, 2, -2, -1],\n [0, -2, -7, 2],\n [4, -1, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 121 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-9, 8, -4, 6],\n [8, 11, -10, 5],\n [-4, -10, -5, 4],\n [6, 5, 4, 7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 524 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-2, -2, 8, 6],\n [0, -8, 10, -10],\n [0, 0, 8, -7],\n [0, 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"
}
] | 872 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, -2, 9, 3],\n [-2, 9, 1, -2],\n [9, 1, -3, -8],\n [3, -2, -8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 248 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, 5, -6, 3],\n [5, -3, 4, -10],\n [-6, 4, -7, 0],\n [3, -10, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 425 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[10, 12, 7, 1],\n [0, -2, 5, -3],\n [0, 0, 7, -8],\n [0, 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"
}
] | 260 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-9, 0, -6, 0],\n [0, 2, -3, 4],\n [-6, -3, 12, 6],\n [0, 4, 6, 3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 627 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-9, -9, -5, 0],\n [0, -8, 5, -8],\n [0, 0, -2, 7],\n [0, 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"
}
] | 296 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, 3, -9, 12],\n [0, 4, 5, -4],\n [0, 0, 5, -12],\n [0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 400 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, 7, 6, -12],\n [-6, 11, -5, 5],\n [-10, -1, -5, 9],\n [3, -7, -8, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 368 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[5, -10, 2, -9],\n [0, -5, -2, -7],\n [0, 0, 12, 5],\n [0, 0, 0, 11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 700 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-7, 10, -10, -2],\n [0, -5, 10, 4],\n [0, 0, -3, 12],\n [0, 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"
}
] | 210 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, 8, 9, 2],\n [0, 2, -3, 12],\n [0, 0, 1, 1],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 24 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[3, 2, -9, -10],\n [0, 12, -4, 2],\n [0, 0, 4, -4],\n [0, 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"
}
] | 712 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, -11, 10, 12],\n [7, -3, 2, -2],\n [11, -4, -10, -7],\n [2, -1, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 920 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[1, 0, -2, -4],\n [0, 2, 6, 2],\n [-2, 6, 4, -2],\n [-4, 2, -2, -1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 172 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[12, 4, 6, -4],\n [0, -11, 3, 1],\n [0, 0, 5, 0],\n [0, 0, 0, -11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 260 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-6, 7, -11, -3],\n [0, -1, -6, -6],\n [0, 0, 9, -1],\n [0, 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"
}
] | 892 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[7, 6, -7, -2],\n [11, -7, 9, -8],\n [1, -12, -6, 0],\n [-12, -4, 4, -9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 905 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[1, -10, -1, -12],\n [-10, -12, 6, 2],\n [-1, 6, -9, 1],\n [-12, 2, 1, -8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 600 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[12, 5, -6, 0],\n [-7, -5, 4, -7],\n [-1, -8, 5, -7],\n [11, -11, 9, 10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 793 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, -2, 11, -12],\n [11, -9, -3, 9],\n [-6, 8, 12, 11],\n [5, -12, 2, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 569 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, 8, -4, -2],\n [8, -11, -8, 2],\n [-4, -8, 2, 0],\n [-2, 2, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 704 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, -2, -6, -6],\n [-2, -2, 6, -6],\n [-6, 6, -12, 2],\n [-6, -6, 2, 5]]\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[[4, -3, 8, -1],\n [0, -5, -5, 8],\n [0, 0, -2, 1],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 680 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-7, 2, -10, -8],\n [-9, -5, 7, 2],\n [4, -6, 1, -4],\n [-2, -11, 7, 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"
}
] | 386 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[6, 4, 7, 4],\n [4, -12, -6, 10],\n [7, -6, 4, 7],\n [4, 10, 7, -12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 268 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-5, 2, -12, 1],\n [0, 7, 12, -9],\n [0, 0, 1, 12],\n [0, 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"
}
] | 685 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, -7, -1, 11],\n [-5, 12, 0, 10],\n [-8, -10, 5, 6],\n [-11, 8, -2, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, -8, 0, 8],\n [-8, -11, 1, -7],\n [0, 1, -10, -9],\n [8, -7, -9, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 941 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, -5, 4, -11],\n [0, -12, -11, 7],\n [0, 0, -6, -10],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 152 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, 5, 0, 9],\n [0, 7, 6, -8],\n [0, 0, 12, -8],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 380 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, 4, -5, -5],\n [0, 5, -1, -5],\n [0, 0, 9, -12],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, 8, 7, 0],\n [6, 8, 6, 7],\n [-2, 8, 4, -2],\n [-10, -10, -4, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 132 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[9, -1, -12, -11],\n [0, -9, 11, -6],\n [0, 0, 12, 5],\n [0, 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"
}
] | 748 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, -2, -4, 0],\n [11, 8, 9, -12],\n [11, -12, 11, -5],\n [5, 5, -12, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 477 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-8, -7, -8, 10],\n [0, -1, 0, 9],\n [0, 0, -8, 0],\n [0, 0, 0, 12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 232 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, 4, 2, 4],\n [4, -8, -7, 0],\n [2, -7, -4, 2],\n [4, 0, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 922 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, -4, 1, -3],\n [-4, 10, -8, -6],\n [1, -8, -2, 3],\n [-3, -6, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 784 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, -7, -11, -5],\n [4, -3, 9, -7],\n [0, 2, -9, 2],\n [-10, 11, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 926 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[2, 7, -7, 9],\n [0, 10, -4, -4],\n [0, 0, -7, 2],\n [0, 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"
}
] | 840 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-8, 0, 4, 2],\n [0, -9, -7, 11],\n [4, -7, 11, -8],\n [2, 11, -8, -10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 816 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-1, 0, 2, 11],\n [0, 9, -1, -1],\n [0, 0, 11, -12],\n [0, 0, 0, 12]]\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"
}
] | 812 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-2, -2, 3, 0],\n [-2, -3, 6, 9],\n [3, 6, 10, 8],\n [0, 9, 8, -11]]\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"
}
] | 840 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[0, 4, -5, -7],\n [0, 2, 5, -8],\n [-1, 6, 9, 7],\n [-8, -6, 11, -9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 98 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-9, -12, 4, 3],\n [0, 5, -1, -5],\n [0, 0, 5, 3],\n [0, 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"
}
] | 975 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, 7, 1, 0],\n [7, 9, -6, 8],\n [1, -6, -4, 4],\n [0, 8, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 191 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, -12, 8, -1],\n [-4, -4, -12, 10],\n [-11, 4, -6, 9],\n [0, -7, -11, -5]]\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[[-8, -6, -12, -3],\n [-11, 10, 11, 12],\n [-12, 11, 9, -10],\n [8, 10, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 247 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, -2, 8, -3],\n [9, -12, 3, 5],\n [1, 10, -10, -5],\n [7, 11, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 265 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-5, -1, -10, -2],\n [0, -6, 12, 11],\n [0, 0, -9, -10],\n [0, 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"
}
] | 540 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, -10, -3, 7],\n [0, 6, -12, 2],\n [0, 0, 12, 11],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 416 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, 10, -2, -7],\n [0, -11, 2, -10],\n [0, 0, -4, -4],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 904 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-1, -12, 0, 1],\n [0, 7, -12, 0],\n [0, 0, -3, -5],\n [0, 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"
}
] | 84 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-4, 8, -9, 9],\n [7, -8, -1, 0],\n [12, 10, -8, 9],\n [-8, 7, -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"
}
] | 993 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 1, 0, 2],\n [1, -8, 6, 6],\n [0, 6, -10, 0],\n [2, 6, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 454 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[9, 4, 2, 0],\n [4, 10, -6, 0],\n [2, -6, 11, 0],\n [0, 0, 0, 12]]\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"
}
] | 248 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-12, 9, -2, 4],\n [-4, -1, -1, 10],\n [4, 1, 0, 6],\n [-9, -5, 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"
}
] | 486 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-5, 1, 3, 2],\n [1, -9, 4, -8],\n [3, 4, -9, -3],\n [2, -8, -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"
}
] | 870 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-5, 12, 2, 0],\n [0, 1, 3, 0],\n [0, 0, -11, -10],\n [0, 0, 0, 12]]\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"
}
] | 660 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-4, 8, -7, -2],\n [0, -11, -6, -3],\n [0, 0, -9, 2],\n [0, 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"
}
] | 40 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[8, -11, -12, -4],\n [0, 11, 12, -3],\n [0, 0, -7, 7],\n [0, 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"
}
] | 72 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[4, 1, 7, -11],\n [0, -4, 4, 1],\n [0, 0, -5, -4],\n [0, 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"
}
] | 280 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, -8, -10, -9],\n [-8, 9, -6, 0],\n [-10, -6, 2, -2],\n [-9, 0, -2, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 514 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-6, 12, 7, 5],\n [1, 10, -9, -9],\n [6, 8, -3, -6],\n [12, 8, 12, -4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 464 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-12, -7, 2, 8],\n [0, 9, -1, -5],\n [0, 0, -5, -6],\n [0, 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"
}
] | 220 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, -2, -2, 2],\n [-2, -10, 8, 0],\n [-2, 8, 4, 2],\n [2, 0, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 440 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-4, 5, 6, 8],\n [0, -8, 1, 1],\n [0, 0, 8, 1],\n [0, 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"
}
] | 208 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[7, -8, -3, -1],\n [0, 4, -12, 6],\n [0, 0, -2, -8],\n [0, 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"
}
] | 944 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-4, 8, -7, -2],\n [0, -5, -5, -10],\n [-1, 9, 4, -10],\n [4, -10, 10, 12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[9, 4, -6, -8],\n [1, -5, 1, -9],\n [-8, -8, -5, 1],\n [-3, 2, -3, 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"
}
] | 392 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-4, 11, 11, -9],\n [0, -4, -6, 10],\n [0, 0, -3, 4],\n [0, 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"
}
] | 664 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, 8, -3, -2],\n [7, -9, -5, 9],\n [-12, -4, -2, 12],\n [-3, 6, -6, 4]]\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[[9, 1, 12, -7],\n [0, 6, 5, 2],\n [0, 0, 4, -12],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 624 | MATH |
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