messages listlengths 1 1 | ground_truth stringlengths 1 3 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 2, -2, -4],\n [2, -5, 0, -6],\n [-2, 0, -10, 1],\n [-4, -6, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 170 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[12, 12, 8, 6],\n [8, 3, -9, 10],\n [8, -2, 5, -6],\n [-4, 8, 2, -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"
}
] | 768 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[6, -4, 5, -11],\n [1, 6, -12, 10],\n [2, 10, 0, 10],\n [-4, 9, 10, -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"
}
] | 196 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, -5, -8, -7],\n [5, -9, 3, -10],\n [-11, 3, 12, 7],\n [9, 9, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 45 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, 10, 0, -10],\n [-7, -6, 11, 1],\n [10, -6, -2, -9],\n [-7, -5, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 90 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, -7, 0, 7],\n [0, -10, -10, 7],\n [0, 0, 4, 8],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 80 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, -10, 8, 0],\n [-10, -4, -3, 6],\n [8, -3, -5, 6],\n [0, 6, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 448 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-11, -12, -10, 3],\n [-8, -12, 4, -7],\n [12, -7, -3, -5],\n [12, 7, -7, 3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 598 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-2, 7, 12, -2],\n [1, 5, 7, -2],\n [6, -9, -4, -12],\n [-1, 1, 4, -9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 634 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[2, 0, 0, 6],\n [0, 3, -1, 6],\n [0, -1, 8, 7],\n [6, 6, 7, 3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 272 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-12, 8, 12, 7],\n [8, 4, -10, -2],\n [12, -10, 5, -4],\n [7, -2, -4, 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"
}
] | 992 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, -12, 8, 12],\n [0, -9, -10, -9],\n [0, 0, 3, -10],\n [0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 486 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[12, -9, 0, -3],\n [0, -1, 2, -8],\n [0, 0, -6, -6],\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"
}
] | 784 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, -6, -7, 3],\n [0, 2, 10, 11],\n [0, 0, -2, -4],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 988 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[10, 2, -5, -4],\n [-4, -9, -3, 7],\n [-5, -4, -1, 1],\n [-3, 2, 12, 1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 32 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, 7, -5, -9],\n [0, -9, 0, -5],\n [0, 0, -11, 0],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 68 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[10, -1, -7, 12],\n [0, 3, 6, -1],\n [0, 0, 5, -2],\n [0, 0, 0, 12]]? 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 |
[
{
"content": "Compute |A| for the matrix A =\n[[9, -9, -1, 11],\n [12, -9, 6, -6],\n [-5, 3, -10, -5],\n [-3, -1, 1, 11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 544 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, 6, 12, -3],\n [12, -12, -1, -7],\n [8, -8, -11, -12],\n [-3, 0, -12, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 386 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-6, -2, -5, 2],\n [0, 12, -4, -6],\n [0, 0, -3, 7],\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"
}
] | 296 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-12, 10, 8, 3],\n [0, 5, 10, 11],\n [0, 0, -8, 3],\n [0, 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"
}
] | 440 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, 3, 10, 2],\n [3, -10, 4, -3],\n [10, 4, 8, 4],\n [2, -3, 4, -9]]\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[[0, 4, 8, 2],\n [9, -8, 4, -12],\n [-5, 11, -8, 12],\n [2, 5, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 916 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, 8, -9, 2],\n [0, -9, 2, -4],\n [0, 0, 9, -4],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 673 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, -8, 3, 9],\n [0, -2, -7, 11],\n [0, 0, -6, -8],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 108 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, -9, -1, -5],\n [0, -11, -6, 1],\n [0, 0, -11, -1],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 879 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, -3, 7, -2],\n [0, 6, 3, 2],\n [0, 0, -2, 9],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 960 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-2, 3, 0, -4],\n [0, 11, -8, 4],\n [0, 0, -3, -12],\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"
}
] | 462 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-5, -2, 0, 10],\n [-2, 12, -6, -12],\n [0, -6, 11, 10],\n [10, -12, 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"
}
] | 640 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, 4, 11, -8],\n [12, -2, -7, -8],\n [-10, 8, 4, 2],\n [12, -2, -10, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 672 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-10, -3, 2, 6],\n [-3, -5, -10, -2],\n [2, -10, -12, 0],\n [6, -2, 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"
}
] | 392 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, -2, -7, 0],\n [-2, -2, -1, 3],\n [-7, -1, 8, -2],\n [0, 3, -2, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 36 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-12, -6, -6, 4],\n [0, 6, 3, -10],\n [0, 0, -9, 11],\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"
}
] | 536 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, -5, 2, 2],\n [-5, 1, -2, 4],\n [2, -2, 0, -4],\n [2, 4, -4, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 772 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, 5, -8, 2],\n [-12, 7, -9, 10],\n [-3, 9, -9, -8],\n [11, -9, -1, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 141 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[2, -1, 8, 0],\n [-1, 12, 2, -6],\n [8, 2, -5, 0],\n [0, -6, 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"
}
] | 895 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[6, -10, 10, 6],\n [-10, 4, 0, 0],\n [10, 0, 4, 4],\n [6, 0, 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": "Compute |A| for the matrix A =\n[[-4, 0, 2, -10],\n [0, 10, 4, 6],\n [2, 4, 10, -8],\n [-10, 6, -8, -10]]\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": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 3, -2, -4],\n [3, 12, -3, 1],\n [-2, -3, -1, 6],\n [-4, 1, 6, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 113 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[12, -4, 9, -1],\n [-6, 12, 11, -2],\n [-7, 1, -8, -5],\n [-2, 10, -5, -12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 50 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, -3, 5, -2],\n [-3, -10, 0, 4],\n [5, 0, 0, -5],\n [-2, 4, -5, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 525 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-8, -12, -9, 6],\n [-10, -8, -2, -3],\n [-3, -7, -12, -10],\n [-2, -5, -9, 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"
}
] | 617 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[4, -10, -6, 10],\n [4, 10, -2, -1],\n [0, 10, -2, 7],\n [1, 11, 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"
}
] | 784 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, -4, 2, 1],\n [0, -11, 3, -1],\n [0, 0, 6, -12],\n [0, 0, 0, -6]]\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[[-12, -12, -6, 5],\n [-2, -10, -12, -3],\n [11, -4, 7, -7],\n [2, -5, -9, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 322 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, 11, -1, 7],\n [0, 10, 2, -9],\n [0, 0, -3, -3],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 350 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[1, -3, -6, 0],\n [0, -12, -12, -1],\n [0, 0, 7, 1],\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"
}
] | 580 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[7, -7, 8, -4],\n [0, 1, 3, 1],\n [0, 0, 1, 11],\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"
}
] | 7 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, -10, 2, -7],\n [0, 7, -10, -11],\n [0, 0, 6, 8],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 940 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[12, -12, 9, 10],\n [0, 5, -12, 9],\n [0, 0, 9, 8],\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"
}
] | 160 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-3, 0, -2, -2],\n [0, -5, -8, -3],\n [-2, -8, -3, -8],\n [-2, -3, -8, -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"
}
] | 803 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-5, 8, -3, -4],\n [0, -10, 12, 4],\n [0, 0, 3, -3],\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"
}
] | 350 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[0, -10, -11, -2],\n [1, -4, -6, 5],\n [-9, 0, -1, 11],\n [3, 2, -6, 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"
}
] | 120 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, -3, -3, 5],\n [0, 3, -12, -2],\n [0, 0, 3, 0],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 28 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-2, -2, -8, 7],\n [-2, 6, 4, 2],\n [-8, 4, 5, 0],\n [7, 2, 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"
}
] | 834 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-10, 4, -4, -2],\n [4, -5, 3, -4],\n [-4, 3, 6, -6],\n [-2, -4, -6, 11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 302 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-6, 8, -6, -6],\n [0, -6, -8, 7],\n [0, 0, -5, -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"
}
] | 980 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-5, -7, 9, 12],\n [0, -6, -7, -11],\n [0, 0, 12, -6],\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"
}
] | 520 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[7, 4, -10, 1],\n [0, 5, 1, -7],\n [0, 0, -1, -4],\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"
}
] | 105 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[4, 3, -2, -8],\n [3, 4, -7, 5],\n [-2, -7, 4, 12],\n [-8, 5, 12, 3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 528 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-5, -9, 1, 9],\n [10, -12, -1, 3],\n [0, 12, -9, 8],\n [-6, -2, -9, -5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 806 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-2, 8, -2, -2],\n [8, -2, -2, 9],\n [-2, -2, 5, 3],\n [-2, 9, 3, -10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 474 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-1, 3, -8, -12],\n [0, 3, -7, 8],\n [0, 0, 12, -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"
}
] | 604 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[9, 7, -8, 8],\n [0, 6, 1, 11],\n [0, 0, 12, 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"
}
] | 944 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, -11, 5, -8],\n [9, 7, -1, -6],\n [-6, -8, -1, -1],\n [12, -5, 8, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 190 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[2, 8, -5, -1],\n [8, 0, -7, 6],\n [-5, -7, 11, 4],\n [-1, 6, 4, -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"
}
] | 765 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, -3, 4, 5],\n [0, 6, 8, 1],\n [0, 0, 3, 1],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 424 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[5, -3, -10, 7],\n [-5, 6, -1, -6],\n [-3, 4, 10, -5],\n [-5, -12, -7, 6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 602 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-6, 6, 4, -2],\n [-5, 9, -6, -5],\n [1, -5, -1, -12],\n [-10, -7, -12, -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"
}
] | 796 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-10, -8, 6, 2],\n [7, 12, -2, 2],\n [-5, 4, -5, -6],\n [-6, 0, 6, -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"
}
] | 440 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-2, 10, 11, -2],\n [0, 12, 11, 12],\n [0, 0, 12, -11],\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"
}
] | 592 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, 8, 5, 4],\n [4, -9, 7, 1],\n [0, 4, -2, 8],\n [4, -11, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 656 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, -11, 2, -5],\n [11, -3, -12, -7],\n [-5, 6, -11, -2],\n [-10, 7, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 375 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-2, 4, -2, 5],\n [4, -5, 2, -6],\n [-2, 2, -3, 2],\n [5, -6, 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"
}
] | 143 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-3, -5, -2, 12],\n [0, -12, -5, 7],\n [0, 0, -3, -2],\n [0, 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"
}
] | 108 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, -10, -1, -3],\n [4, -2, 0, 7],\n [-2, 5, -8, 10],\n [-2, -12, 12, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 58 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[12, 7, -6, -2],\n [0, -6, 10, 12],\n [0, 0, 2, 9],\n [0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 848 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-12, 7, -11, 2],\n [0, -1, -10, -9],\n [0, 0, 6, 11],\n [0, 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"
}
] | 216 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 7, -8, -5],\n [6, 0, 0, -6],\n [7, 8, 2, -11],\n [-4, 10, 4, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 528 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, -11, -5, -5],\n [0, 8, -3, 2],\n [0, 0, -1, -5],\n [0, 0, 0, 4]]\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[[10, -4, -4, 9],\n [0, 6, 6, -7],\n [0, 0, 1, -7],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 720 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, -9, 2, 2],\n [2, 12, -11, -2],\n [-9, -3, -4, -8],\n [2, -12, -11, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 874 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, -11, -10, -1],\n [4, -7, 5, 11],\n [10, -3, -2, 7],\n [10, -8, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 710 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, 0, -4, 9],\n [0, -11, 9, 7],\n [0, 0, -9, -4],\n [0, 0, 0, 4]]\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[[0, -1, 2, -2],\n [-1, 8, 7, -4],\n [2, 7, -2, 0],\n [-2, -4, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 900 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-8, -9, -5, 10],\n [6, -4, -8, 11],\n [0, 3, -12, -9],\n [10, 10, -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"
}
] | 522 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-8, -8, -10, 1],\n [0, 9, -12, 3],\n [0, 0, 3, -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"
}
] | 944 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, 2, -3, 3],\n [7, -3, -12, 11],\n [7, 8, 11, 1],\n [-7, 12, -9, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 770 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[7, 6, -4, -5],\n [0, 2, -2, -4],\n [0, 0, -3, 4],\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"
}
] | 504 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[12, -5, 2, -4],\n [-5, -6, 4, -6],\n [2, 4, 8, 2],\n [-4, -6, 2, -3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 348 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, -2, 4, -9],\n [-2, -10, 8, 6],\n [4, 8, 5, -8],\n [-9, 6, -8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 626 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[12, 5, -8, 5],\n [-2, 6, -1, -11],\n [2, -6, 2, -12],\n [0, 9, -8, 5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 216 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[0, 0, 6, -11],\n [0, -8, -2, -4],\n [6, -2, -2, 4],\n [-11, -4, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 828 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[9, 5, -6, -4],\n [0, -7, 3, -6],\n [0, 0, 3, -11],\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"
}
] | 299 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, 0, -10, 4],\n [-8, 5, 8, 2],\n [9, 8, 7, 5],\n [4, 2, -7, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 184 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-2, -2, -4, -1],\n [0, 5, 11, 7],\n [0, 0, 1, -11],\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"
}
] | 990 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, 1, 4, 10],\n [0, -1, -8, 2],\n [0, 0, 8, -1],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 72 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, 9, 11, 2],\n [6, -12, 5, 6],\n [-8, 11, 6, -10],\n [-3, -6, 12, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 782 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-12, 4, -11, -6],\n [0, 10, -8, 7],\n [0, 0, 8, 7],\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"
}
] | 920 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, 5, 1, 3],\n [-7, 1, -11, 3],\n [4, -10, 11, 9],\n [8, -7, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 892 | MATH |
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