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[[-2, -4, -8, 1],\n [0, 9, -3, 2],\n [0, 0, 1, -11],\n [0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 910 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[9, -7, 5, -3],\n [0, -8, 10, 10],\n [0, 0, 8, -10],\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"
}
] | 152 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-1, -2, -8, 7],\n [0, 12, -7, -10],\n [0, 0, 4, 8],\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"
}
] | 192 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, -10, 4, 1],\n [-9, -4, -9, 2],\n [-2, 0, -11, -12],\n [-2, 5, 9, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 771 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-10, 2, 4, 6],\n [0, -5, 6, 12],\n [0, 0, 12, 7],\n [0, 0, 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"
}
] | 600 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, -10, 9, -8],\n [0, -8, -6, 0],\n [0, 0, 7, -8],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 72 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, 0, -12, 1],\n [0, -11, 6, 5],\n [0, 0, -4, 1],\n [0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 760 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, 6, 0, -11],\n [4, -10, -10, 3],\n [-9, 9, 11, 10],\n [-12, 6, -10, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 48 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[0, -5, 1, 1],\n [-5, 9, -4, 2],\n [1, -4, 0, 6],\n [1, 2, 6, 6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 110 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[2, 4, -2, 2],\n [0, 11, 3, 6],\n [0, 0, 1, 5],\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"
}
] | 154 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[0, 8, 2, 10],\n [8, 1, 9, -12],\n [2, 9, 7, 2],\n [10, -12, 2, -4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 736 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-9, -6, 10, 7],\n [-6, 10, 2, 6],\n [10, 2, -7, 11],\n [7, 6, 11, -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"
}
] | 386 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[11, -10, -4, -2],\n [-10, 9, 6, 1],\n [-4, 6, -1, -4],\n [-2, 1, -4, -3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 440 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, 0, -12, 1],\n [-10, -7, -1, -8],\n [6, -4, -2, 9],\n [-10, -6, -3, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 393 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, -11, 5, 12],\n [-3, 9, -4, -5],\n [-7, 11, 10, 1],\n [-10, -12, -5, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 146 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-8, -3, -9, 7],\n [0, 11, 10, -7],\n [0, 0, -1, 4],\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"
}
] | 912 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[3, -3, -2, -9],\n [-3, -10, 8, -2],\n [-2, 8, 7, 5],\n [-9, -2, 5, -3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 248 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-2, 3, 3, 4],\n [0, -10, -9, 8],\n [0, 0, -3, 12],\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"
}
] | 480 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[5, -3, 11, -3],\n [-9, 2, 10, 11],\n [3, 6, 2, 6],\n [-11, 2, -12, 11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 574 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, -7, -10, 2],\n [-3, 5, -4, 5],\n [12, 2, -8, 4],\n [-9, -1, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 824 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-12, 2, 6, -2],\n [2, -5, 2, 0],\n [6, 2, 8, 0],\n [-2, 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"
}
] | 556 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, -4, 8, 0],\n [-4, -11, 0, 6],\n [8, 0, 0, -2],\n [0, 6, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 532 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[11, -12, 7, -7],\n [-7, 6, -8, 3],\n [6, 1, -2, 9],\n [-11, -6, -11, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 643 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-5, 12, -2, 3],\n [6, -4, 6, -3],\n [-5, -3, 9, -10],\n [8, -8, -8, -12]]\nRound to the nearest integer, then take the result modulo 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[[-9, 8, 6, 4],\n [0, 10, 8, -11],\n [0, 0, 7, -10],\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"
}
] | 220 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, 9, 5, 4],\n [0, 1, -9, -1],\n [0, 0, 7, -9],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 496 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[6, -6, 1, 7],\n [-4, 8, 2, 12],\n [-12, -7, 0, -7],\n [10, 0, -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"
}
] | 604 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-2, 8, -6, -5],\n [8, -10, 0, 7],\n [-6, 0, -11, -9],\n [-5, 7, -9, 0]]? 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": "What is the determinant of the matrix:\n[[1, -11, -5, -6],\n [0, -11, 12, -7],\n [0, 0, 12, 1],\n [0, 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"
}
] | 604 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-11, 4, -7, 5],\n [4, -2, -1, -8],\n [-7, -1, -12, -10],\n [5, -8, -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"
}
] | 260 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, -9, 3, 4],\n [-9, -6, 7, 2],\n [3, 7, -2, 2],\n [4, 2, 2, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 892 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-12, -9, 1, 1],\n [0, 6, 10, 7],\n [0, 0, 8, -11],\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"
}
] | 848 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, -3, -3, -8],\n [-9, -11, 9, -5],\n [-5, 2, 3, -11],\n [-12, -8, 8, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 826 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, -10, -1, -6],\n [-10, -2, -3, 1],\n [-1, -3, 12, 2],\n [-6, 1, 2, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 749 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-8, -9, 1, 2],\n [0, 5, 3, 3],\n [0, 0, 8, 0],\n [0, 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"
}
] | 760 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-6, -6, 7, -1],\n [0, 3, 4, 11],\n [0, 0, 7, 5],\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"
}
] | 126 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, 12, 0, -4],\n [-4, -7, -6, 3],\n [-10, 0, -5, -3],\n [4, 12, 8, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 853 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 9, 11, 11],\n [5, -8, 3, 6],\n [-1, -6, -3, -8],\n [7, -10, 10, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 560 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[3, 3, 7, -3],\n [-3, 0, -4, 7],\n [6, 8, 7, 2],\n [-2, 11, 7, 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"
}
] | 225 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[12, 3, 0, -4],\n [-7, -8, 12, -9],\n [2, -4, -2, -7],\n [-3, -5, 11, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 963 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-8, -8, -2, -9],\n [0, -3, 6, -11],\n [0, 0, 10, -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"
}
] | 840 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[6, 6, 9, -5],\n [6, -7, -5, 6],\n [9, -5, -12, 8],\n [-5, 6, 8, -6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 343 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, -8, -12, 2],\n [-7, -12, -11, 5],\n [0, 9, -3, -1],\n [2, -4, 10, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 64 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[6, -7, 4, 9],\n [0, 6, 6, -6],\n [0, 0, 8, -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"
}
] | 152 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 3, -7, 11],\n [7, -1, 6, -2],\n [-7, 2, -6, -1],\n [3, -1, 7, 11]]\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[[-8, -6, 1, 6],\n [-6, 6, 10, 1],\n [1, 10, 5, -4],\n [6, 1, -4, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 389 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-7, 11, -4, 3],\n [4, -3, -7, 8],\n [7, 3, 6, 4],\n [-5, -12, -7, 10]]\nRound to the nearest integer, then take the result 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[[1, 3, -2, 1],\n [12, 5, 11, -12],\n [-4, 8, -10, -6],\n [-11, 0, 7, -12]]? Round to the nearest integer, then express your answer modulo 1000.\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[[6, -7, 2, 1],\n [0, 4, 6, -6],\n [0, 0, -12, 0],\n [0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 120 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-3, -6, -7, 5],\n [6, -9, -11, -3],\n [7, -5, -8, -2],\n [4, -5, 8, -1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 886 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-7, 9, -12, 10],\n [0, -5, 12, 4],\n [0, 0, 4, -6],\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"
}
] | 20 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-5, -11, 4, 5],\n [0, -9, 11, -2],\n [0, 0, 6, -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"
}
] | 110 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[5, -8, -1, 2],\n [-8, 3, 0, 5],\n [-1, 0, -7, 10],\n [2, 5, 10, 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"
}
] | 484 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[11, -5, -8, -2],\n [-5, 3, -4, 0],\n [-8, -4, 2, 10],\n [-2, 0, 10, 2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 656 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-2, -3, -10, 1],\n [-3, 9, 8, -4],\n [11, 5, 8, 5],\n [-2, -5, 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"
}
] | 570 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[2, -2, -2, 3],\n [-11, 8, 6, -10],\n [-5, -11, -5, 8],\n [-4, 4, -8, -11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 880 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, -5, 0, -4],\n [-5, -2, 0, -2],\n [0, 0, -1, 0],\n [-4, -2, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 193 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-4, 3, -10, 10],\n [0, -9, 4, -5],\n [0, 0, 1, -10],\n [0, 0, 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"
}
] | 396 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-6, 5, -7, 0],\n [2, 3, -2, 11],\n [11, 2, 8, 7],\n [4, -8, -8, -3]]\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": "What is the determinant of the matrix:\n[[10, -1, -2, -5],\n [0, -2, -2, 11],\n [0, 0, 7, -1],\n [0, 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"
}
] | 420 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-5, 8, -6, 8],\n [8, 5, -2, -6],\n [-6, -2, -4, -4],\n [8, -6, -4, -6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 112 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-5, 9, -2, 2],\n [0, -8, -9, 4],\n [0, 0, 4, -5],\n [0, 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"
}
] | 480 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-3, 12, -4, -6],\n [0, 2, 7, 4],\n [0, 0, 5, -7],\n [0, 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"
}
] | 240 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-12, 9, -5, -6],\n [-12, -4, -9, 10],\n [7, -1, 5, -9],\n [-9, -1, -8, 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"
}
] | 517 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-8, 0, -6, 3],\n [0, -5, -4, 0],\n [-6, -4, -8, 0],\n [3, 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"
}
] | 868 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-4, 8, 6, 11],\n [12, -12, 0, -7],\n [4, -12, -12, 11],\n [-9, 12, -8, 2]]\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": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, -12, -6, 11],\n [12, -12, 1, -9],\n [-11, 5, -8, 1],\n [8, -10, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 776 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[8, -2, -8, 10],\n [-2, -9, 0, 2],\n [-8, 0, 6, 2],\n [10, 2, 2, -5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 440 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, 3, -11, 11],\n [0, 1, 5, 9],\n [0, 0, -5, 2],\n [0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 650 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[6, 1, -5, 11],\n [0, -7, 12, 1],\n [0, 0, -1, -12],\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"
}
] | 462 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-1, -9, 2, 8],\n [-9, -4, 4, -2],\n [2, 4, -6, -3],\n [8, -2, -3, -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"
}
] | 325 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-9, 11, 8, 10],\n [-5, -4, 1, -10],\n [11, -10, 1, 3],\n [-2, -1, -8, 11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 73 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, -7, -1, 0],\n [0, -8, 4, -4],\n [0, 0, 1, 1],\n [0, 0, 0, 11]]\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[[-3, -7, 2, -9],\n [0, -4, -6, 3],\n [0, 0, -9, 3],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 972 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[2, -11, 4, 7],\n [1, 4, 6, 6],\n [-6, -8, 11, -3],\n [-8, -11, -11, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 560 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[2, 9, 6, -5],\n [-12, -7, -7, 4],\n [-4, -6, -8, 4],\n [-3, 12, -7, -2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 350 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[12, 6, 3, 7],\n [6, 9, -3, -4],\n [3, -3, -11, 6],\n [7, -4, 6, 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"
}
] | 541 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[6, 12, -8, -12],\n [12, -8, -6, 1],\n [-8, -6, -3, -9],\n [-12, 1, -9, -5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 554 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[2, -7, 0, 7],\n [-7, -6, -6, -10],\n [10, -7, 2, 11],\n [7, -10, -6, 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"
}
] | 930 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[8, -3, 8, 0],\n [0, 4, -11, 8],\n [0, 0, 12, 5],\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"
}
] | 768 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-6, -5, -5, -6],\n [0, 10, -10, -3],\n [0, 0, -2, -2],\n [0, 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"
}
] | 40 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 0, -3, -1],\n [0, -5, 5, -6],\n [0, 0, 12, 2],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 200 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-6, -10, -4, 4],\n [-10, 9, -2, 4],\n [-4, -2, 9, -2],\n [4, 4, -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"
}
] | 380 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, -6, 3, -1],\n [0, -10, -3, 10],\n [0, 0, -8, -2],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 320 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[7, 10, 4, -10],\n [10, -8, 6, 7],\n [11, -5, 10, -3],\n [-10, 7, -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"
}
] | 142 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[11, -1, 11, 11],\n [0, -7, -7, 2],\n [0, 0, -3, -1],\n [0, 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"
}
] | 152 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, -11, -9, -11],\n [0, -12, 9, 10],\n [0, 0, 3, 4],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 732 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, -11, -7, -7],\n [-5, 1, 10, 9],\n [-2, 1, -10, 3],\n [-12, -3, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 686 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-12, 0, 6, 4],\n [0, 8, -5, 9],\n [6, -5, 10, 6],\n [4, 9, 6, 6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 468 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[12, -2, 2, 3],\n [-2, 10, -10, 0],\n [2, -10, 2, -6],\n [3, 0, -6, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 336 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[11, -6, -3, 8],\n [0, -1, 11, 4],\n [0, 0, 12, -12],\n [0, 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"
}
] | 208 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, 4, -5, -6],\n [4, 5, 3, 2],\n [-5, 3, -1, -2],\n [-6, 2, -2, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 589 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-9, 2, -10, 6],\n [-4, 4, 6, -5],\n [4, 4, -3, -1],\n [4, 6, 7, 6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 230 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-10, -9, -2, 4],\n [-9, 7, -4, 4],\n [-2, -4, 1, -2],\n [4, 4, -2, 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"
}
] | 550 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[9, 1, -7, 8],\n [0, -5, 4, -6],\n [0, 0, -5, 5],\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"
}
] | 475 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[9, 12, 12, 0],\n [11, -7, -3, -6],\n [4, 12, 7, -3],\n [6, 7, 9, -10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 138 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-4, -11, -8, 12],\n [0, -9, -6, 2],\n [0, 0, 8, -5],\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"
}
] | 832 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[2, 2, 0, 2],\n [2, 9, -2, 5],\n [0, -2, 8, 6],\n [2, 5, 6, -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"
}
] | 376 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, -12, 6, -6],\n [0, 11, 12, 2],\n [0, 0, 2, 4],\n [0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 680 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-2, 10, 6, 1],\n [0, 11, -1, -4],\n [0, 0, 12, -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"
}
] | 264 | MATH |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.