messages listlengths 1 1 | ground_truth stringclasses 992
values | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Determine the value of det(A) where A =\n[[-9, -11, 0, 11],\n [0, 9, -2, 2],\n [0, 0, -7, 4],\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"
}
] | 804 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[12, -6, 8, -1],\n [0, -3, -2, 4],\n [0, 0, 1, -6],\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"
}
] | 604 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, -6, 0, -2],\n [-6, 2, 2, 0],\n [0, 2, 3, 2],\n [-2, 0, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 392 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, 2, 5, -2],\n [-9, 0, 1, 0],\n [-12, 12, 6, -5],\n [-2, -11, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 312 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[5, 9, 2, -12],\n [0, 8, 6, 5],\n [0, 0, -4, 9],\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"
}
] | 640 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[0, 10, 9, 2],\n [-2, -6, 1, -6],\n [-1, 1, -5, -5],\n [-7, 12, 6, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 582 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, 12, -8, -6],\n [-2, 12, 12, 9],\n [-2, 4, 8, -12],\n [7, 6, 7, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 924 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-7, -4, 0, 9],\n [-4, -10, -8, -10],\n [0, -8, -9, -3],\n [9, -10, -3, 1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 678 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, 0, 3, -5],\n [0, -5, 1, -3],\n [3, 1, -5, -5],\n [-5, -3, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 605 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-10, 4, -7, 0],\n [4, -3, -4, 1],\n [-7, -4, -1, -4],\n [0, 1, -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"
}
] | 822 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-6, -3, -5, -4],\n [0, -1, -5, 5],\n [0, 0, 2, -7],\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"
}
] | 48 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[6, -10, 11, -11],\n [-2, 12, 3, -5],\n [5, 4, -7, 2],\n [11, -9, -11, 3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 504 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[5, 0, 3, 4],\n [0, 4, -2, 3],\n [3, -2, -10, -9],\n [4, 3, -9, -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"
}
] | 227 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[7, 6, -3, -11],\n [-10, 3, 0, 6],\n [-7, 10, 10, 9],\n [-4, 5, 9, 9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 613 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[0, 0, 8, -2],\n [0, -8, 1, 6],\n [8, 1, -8, 6],\n [-2, 6, 6, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 388 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, -9, 8, -8],\n [0, -2, 7, -1],\n [0, 0, -7, 1],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 706 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, -7, -1, 8],\n [3, 10, 7, -3],\n [-8, -7, -9, -1],\n [-8, -7, -12, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 369 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[10, -10, 2, -1],\n [0, 1, 5, -7],\n [0, 0, -4, 9],\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"
}
] | 400 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[8, -5, 12, -2],\n [5, -8, 4, -3],\n [-6, -1, 2, -10],\n [-12, -1, -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"
}
] | 156 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-4, -3, 7, 5],\n [-3, -11, -3, -9],\n [7, -3, 7, -6],\n [5, -9, -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"
}
] | 67 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, -2, -2, -5],\n [-2, 8, 4, -3],\n [-2, 4, -3, 1],\n [-5, -3, 1, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 31 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[10, 12, -7, 12],\n [-11, 4, -3, 8],\n [12, 6, 11, 9],\n [4, -5, 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"
}
] | 927 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[6, -6, 9, 1],\n [0, -12, -10, 4],\n [0, 0, 12, 11],\n [0, 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"
}
] | 728 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-11, -6, 4, 4],\n [-6, 3, -4, -1],\n [4, -4, -5, -2],\n [4, -1, -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"
}
] | 844 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-10, -1, -11, 1],\n [-7, 4, 0, 10],\n [-1, -11, 11, 3],\n [8, 2, 7, -9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 558 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[5, -2, 7, 4],\n [-9, 6, 2, 9],\n [2, -5, -3, -12],\n [9, 5, -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"
}
] | 161 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[4, 1, 8, -2],\n [0, 10, 3, 10],\n [0, 0, 9, -6],\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"
}
] | 560 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, -8, 9, 0],\n [-8, -4, -8, -10],\n [9, -8, 4, -2],\n [0, -10, -2, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 980 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-8, 11, -5, 5],\n [-7, -10, 1, -3],\n [-11, -7, 0, 0],\n [1, 10, -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"
}
] | 284 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, -7, 8, -4],\n [0, 5, 4, 6],\n [0, 0, 2, -2],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 970 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, 8, -8, -6],\n [0, 7, -6, -4],\n [0, 0, 7, -1],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, 2, 6, 10],\n [2, 2, -2, 6],\n [6, -2, 7, -10],\n [10, 6, -10, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 90 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[6, 2, -6, 2],\n [2, -11, 1, -4],\n [-6, 1, 4, -7],\n [2, -4, -7, 1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 880 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[7, 7, 5, 3],\n [0, 6, -11, -3],\n [0, 0, -6, -10],\n [0, 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"
}
] | 488 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[3, -6, -4, -4],\n [-6, 11, 8, -2],\n [-4, 8, 2, 11],\n [-4, -2, 11, -1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 33 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[1, -10, 10, 6],\n [-2, 0, -10, 10],\n [-6, 12, -6, -12],\n [10, -8, 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"
}
] | 624 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[12, 9, -7, -10],\n [1, 12, 4, -3],\n [4, -4, -2, 1],\n [5, 2, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 572 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, 5, -11, 3],\n [0, -6, -4, -6],\n [0, 0, -6, -2],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 720 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, 6, 12, 11],\n [2, -3, 11, 9],\n [11, -10, -7, 3],\n [5, 0, -9, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 324 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-5, 2, -6, 4],\n [2, -2, 0, -5],\n [-6, 0, -11, -10],\n [4, -5, -10, -4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 669 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, -12, 8, 2],\n [9, -7, 9, -11],\n [8, 3, 8, 8],\n [4, 10, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 609 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-2, 4, 2, -4],\n [4, -1, -8, 2],\n [2, -8, -8, -2],\n [-4, 2, -2, 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"
}
] | 272 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-3, -1, -5, -8],\n [-1, 10, -7, 1],\n [-5, -7, -6, -2],\n [-8, 1, -2, -8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 579 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, 8, -10, -5],\n [7, -8, -1, 7],\n [8, 9, 8, -5],\n [9, 2, -11, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 212 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 0, 4, -2],\n [0, 8, -8, 2],\n [4, -8, -8, 3],\n [-2, 2, 3, -12]]\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[[4, 1, 8, -6],\n [0, -11, 1, -4],\n [0, 0, -7, -2],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 848 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-11, -9, 0, -4],\n [9, -7, 1, -9],\n [3, 7, 10, 7],\n [7, 6, -10, -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"
}
] | 105 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[5, -8, 4, -2],\n [-8, -5, 0, 4],\n [4, 0, -10, -4],\n [-2, 4, -4, -4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 776 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-8, -4, 0, -1],\n [-4, -10, -3, -2],\n [0, -3, 10, -7],\n [-1, -2, -7, -6]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 365 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, -8, -12, -5],\n [-5, 5, -6, 6],\n [10, 9, -4, -2],\n [-2, -5, -9, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 793 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[6, -7, 4, 10],\n [0, 5, 7, 4],\n [0, 0, -9, -3],\n [0, 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"
}
] | 80 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, -6, 1, -12],\n [10, 9, 4, 8],\n [2, -11, 6, -1],\n [12, -3, -11, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 125 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[7, -10, -3, 1],\n [-10, -2, -3, -2],\n [-3, -3, 6, -2],\n [1, -2, -2, -6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 763 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[0, -11, 5, 7],\n [-6, 4, -6, -3],\n [12, 0, -1, 2],\n [-8, -12, -2, -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"
}
] | 48 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, 8, 10, -1],\n [5, 9, -4, -9],\n [3, -11, 12, -9],\n [8, -12, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 310 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-11, 8, 2, -10],\n [8, 0, 8, -2],\n [2, 8, -6, -4],\n [-10, -2, -4, -11]]\nRound to the nearest integer, then take the result 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[[11, 0, -11, -11],\n [-11, 6, -1, -10],\n [-10, -12, -5, -10],\n [-1, -4, -1, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 708 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[4, -1, -2, -2],\n [-1, -5, 12, 2],\n [-2, 12, 5, 6],\n [-2, 2, 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"
}
] | 922 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[5, 3, 3, 10],\n [5, -12, -3, -6],\n [8, 5, -6, 7],\n [3, 6, 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"
}
] | 676 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, -4, 0, -6],\n [2, 6, 1, 2],\n [2, 0, 6, 4],\n [11, -10, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 288 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-4, -7, 7, -12],\n [0, -7, -10, -6],\n [0, 0, 5, 5],\n [0, 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"
}
] | 580 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[4, 9, 11, -1],\n [0, 11, 4, 7],\n [0, 0, 3, 2],\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"
}
] | 812 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, 8, -8, 7],\n [0, 2, 10, -2],\n [0, 0, 2, 10],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 856 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, -6, 4, -2],\n [-6, 8, 10, 0],\n [4, 10, -4, -1],\n [-2, 0, -1, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 908 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-4, -1, -6, 2],\n [1, 7, -4, 9],\n [-5, 5, -1, -11],\n [5, -10, -12, 9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 702 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-9, -4, 5, 5],\n [-4, -1, 2, 7],\n [-7, 7, 6, 7],\n [10, -7, -12, -12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 777 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[10, 5, -5, -6],\n [11, 8, 11, 3],\n [-2, -9, -6, 12],\n [3, -11, 1, 2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 81 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[12, 10, 5, 9],\n [0, 12, 6, 4],\n [0, 0, -1, -9],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 584 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[1, 4, -6, -2],\n [4, 5, 0, 1],\n [-6, 0, -11, -1],\n [-2, 1, -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"
}
] | 640 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[10, 4, 8, -6],\n [4, -1, 2, 0],\n [8, 2, -4, 2],\n [-6, 0, 2, 7]]? 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": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 3, 0, -9],\n [-3, -11, -9, 3],\n [7, 3, 5, 11],\n [0, 8, 8, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 192 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, -11, -9, 8],\n [-7, -10, -3, 3],\n [8, 9, -1, 4],\n [6, -2, -10, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 201 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-10, 7, 7, -5],\n [0, -10, 0, -4],\n [0, 0, 12, -7],\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"
}
] | 200 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[11, 4, 1, -2],\n [4, 5, 6, 8],\n [1, 6, 8, 6],\n [-2, 8, 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"
}
] | 670 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, -6, 8, 11],\n [0, -3, -4, 1],\n [0, 0, -3, -7],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 946 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 6, 6, 0],\n [6, 4, -2, 8],\n [6, -2, 12, 2],\n [0, 8, 2, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 428 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, -10, 4, -2],\n [0, 1, -5, 0],\n [0, 0, 9, 5],\n [0, 0, 0, 8]]\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, -3, -4],\n [0, 6, 7, -8],\n [0, 0, -3, -9],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 136 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, -7, 6, 8],\n [-5, 0, -11, 0],\n [1, 10, -8, 1],\n [-11, 5, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 306 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[6, 9, 3, 0],\n [9, 7, 2, -6],\n [3, 2, -5, 2],\n [0, -6, 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"
}
] | 840 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[12, 1, 2, 6],\n [1, 6, 4, 4],\n [2, 4, -6, -1],\n [6, 4, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 125 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, 7, -6, -1],\n [10, 11, 6, 4],\n [-2, 3, -11, -11],\n [-5, 4, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 439 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[0, -7, -8, -3],\n [-7, -7, -2, 4],\n [-8, -2, 4, -5],\n [-3, 4, -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"
}
] | 93 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-10, -10, -2, 5],\n [-10, 12, -6, -2],\n [-2, -6, -12, 0],\n [5, -2, 0, 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"
}
] | 708 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-3, -5, 3, -6],\n [0, -3, -10, 12],\n [0, 0, 6, 0],\n [0, 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"
}
] | 108 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, 4, -10, 1],\n [4, -12, 11, 0],\n [-10, 11, 7, 0],\n [1, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 949 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-12, 4, 7, 4],\n [4, 7, -2, 6],\n [7, -2, 2, 0],\n [4, 6, 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"
}
] | 668 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-9, -4, 0, -8],\n [-3, -2, -6, -3],\n [-4, 4, -3, 3],\n [11, 3, -8, 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"
}
] | 747 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[9, -2, 8, 0],\n [5, 10, -5, -3],\n [-12, 1, 12, 6],\n [-1, -8, 5, 4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 393 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, 8, -2, 5],\n [8, -11, -2, 7],\n [-2, -2, 4, 9],\n [5, 7, 9, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 222 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, 2, 0, 0],\n [2, 6, 2, -7],\n [0, 2, -12, -6],\n [0, -7, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 304 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[3, -1, 10, 2],\n [0, -11, -4, 0],\n [0, 0, 12, 7],\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"
}
] | 228 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, 3, 2, -3],\n [-11, -3, -1, -10],\n [5, -6, 7, 7],\n [-5, 0, 12, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 829 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-11, -7, 9, 11],\n [6, -8, -1, 12],\n [0, -4, 9, -2],\n [11, 11, 10, 1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 436 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[3, -6, -9, -3],\n [0, 10, -1, -4],\n [0, 0, -8, -6],\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"
}
] | 400 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[9, 5, 6, 0],\n [5, -7, -1, 6],\n [6, -1, 4, -3],\n [0, 6, -3, 5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 351 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, 4, 4, -1],\n [4, 12, 2, 0],\n [4, 2, 9, -8],\n [-1, 0, -8, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 408 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-3, -1, 1, -2],\n [0, -5, 5, 10],\n [0, 0, 7, -11],\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"
}
] | 580 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, 3, 12, 3],\n [-7, 11, -12, -5],\n [5, -12, -8, -12],\n [6, 7, 9, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[10, 10, -3, 6],\n [0, 1, -8, 1],\n [0, 0, 5, 1],\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"
}
] | 800 | MATH |
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