messages listlengths 1 1 | ground_truth stringclasses 992
values | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Determine the value of det(A) where A =\n[[-10, 11, -5, 6],\n [8, -1, -2, 8],\n [10, -7, 5, 5],\n [-10, 9, -5, -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"
}
] | 560 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, -6, 12, -7],\n [8, -2, 2, -4],\n [9, 2, -4, 5],\n [1, 2, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 598 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, -1, 11, -1],\n [3, -2, -7, -5],\n [7, 12, 10, 8],\n [-11, -12, -11, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 930 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[2, -5, 4, -7],\n [8, 7, 3, -7],\n [3, -9, 2, 7],\n [-10, 12, 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"
}
] | 480 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, 4, 5, -10],\n [4, -9, 3, 4],\n [5, 3, 4, 5],\n [-10, 4, 5, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 557 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, -3, -5, 6],\n [-3, -9, 0, -1],\n [-5, 0, 12, 1],\n [6, -1, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 51 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[12, 2, 5, 2],\n [2, -4, -2, -4],\n [5, -2, -5, 10],\n [2, -4, 10, 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"
}
] | 480 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[9, -7, -3, -7],\n [0, -8, 5, 1],\n [0, 0, 11, 1],\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"
}
] | 752 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, -8, -4, -11],\n [10, 7, -4, -6],\n [-11, 5, 10, 10],\n [-8, 9, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 705 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-10, 0, 1, 0],\n [0, -1, -4, 8],\n [1, -4, 8, 2],\n [0, 8, 2, 1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 665 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-11, -2, -8, -1],\n [-7, -8, -9, -2],\n [2, -6, 3, -2],\n [2, 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"
}
] | 44 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, 0, 1, -1],\n [0, -11, -2, -6],\n [1, -2, -12, 1],\n [-1, -6, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 437 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, -1, -12, 2],\n [0, -5, -3, 9],\n [0, 0, -11, 12],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 845 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[5, 2, -11, 12],\n [0, 4, 4, -11],\n [0, 0, -8, 11],\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"
}
] | 40 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[10, -9, -5, 3],\n [-2, 4, 5, -9],\n [-4, -4, -6, -6],\n [-7, -8, 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"
}
] | 916 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[8, -6, -7, 2],\n [-6, -3, -4, -2],\n [-7, -4, 7, 10],\n [2, -2, 10, 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"
}
] | 887 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-4, -10, -2, 7],\n [-10, 11, -12, -1],\n [-4, -4, -6, 8],\n [-1, -12, 7, -7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 762 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-11, -12, 7, 8],\n [0, 6, 6, 2],\n [0, 0, 10, 0],\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"
}
] | 40 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[6, 3, 6, -8],\n [3, 3, -4, 8],\n [6, -4, -7, -12],\n [-8, 8, -12, -11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 25 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-4, -2, -6, 0],\n [-2, -12, 1, 8],\n [-6, 1, -1, 0],\n [0, 8, 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"
}
] | 128 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-4, -11, 8, 8],\n [0, -3, 4, -6],\n [0, 0, -3, 10],\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"
}
] | 36 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, 10, 9, -7],\n [0, -7, 1, -10],\n [0, 0, -10, 8],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 530 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[9, -9, -4, 6],\n [11, -7, -12, 12],\n [8, -7, 3, -1],\n [-12, 12, 10, 0]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 660 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, 6, 3, 2],\n [6, -2, -4, 2],\n [3, -4, -10, -4],\n [2, 2, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 694 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[0, -2, 8, 10],\n [-2, 5, 6, 8],\n [8, 6, 0, -5],\n [10, 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"
}
] | 684 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[4, 0, 2, -6],\n [0, -6, 0, 6],\n [2, 0, 9, 2],\n [-6, 6, 2, 1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 984 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, -8, -1, 0],\n [-8, 7, -4, -2],\n [-1, -4, 7, 4],\n [0, -2, 4, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 304 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-9, -3, -6, 7],\n [0, -9, 8, -7],\n [0, 0, -7, 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"
}
] | 763 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, -12, 12, -10],\n [0, 6, -1, 8],\n [0, 0, 9, -9],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 816 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, 8, 3, 1],\n [1, 3, 2, 0],\n [6, 12, -3, 4],\n [-6, 9, -11, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 879 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-10, -5, -6, -7],\n [0, 9, 7, 9],\n [0, 0, 2, 8],\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"
}
] | 460 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-12, -4, -3, 7],\n [7, -12, 8, 0],\n [-8, -9, -3, -11],\n [5, -9, -3, -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"
}
] | 625 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, -4, -7, 7],\n [0, -10, 1, 4],\n [0, 0, -7, -3],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 490 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[7, -8, 6, -8],\n [2, -8, 10, 5],\n [2, 4, -11, 8],\n [5, 6, 7, 2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 682 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[6, 9, 1, -7],\n [0, 2, 11, -1],\n [0, 0, 3, 12],\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"
}
] | 784 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[12, 12, -1, -12],\n [0, -7, -1, -12],\n [0, 0, 10, -12],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 240 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, 0, -3, -2],\n [0, 6, 2, -2],\n [-3, 2, 6, 4],\n [-2, -2, 4, -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[[-4, 4, 2, 3],\n [4, 1, -1, -6],\n [2, -1, -1, -1],\n [3, -6, -1, 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"
}
] | 26 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-12, 10, 5, -1],\n [10, 6, -8, -6],\n [5, -8, 0, 1],\n [-1, -6, 1, 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"
}
] | 116 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-2, -8, -4, 0],\n [-8, 9, -10, 8],\n [-4, -10, 11, 0],\n [0, 8, 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"
}
] | 516 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, -1, -12, -4],\n [0, -3, 6, -10],\n [0, 0, 10, -1],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 670 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-8, -3, 10, -3],\n [9, 3, -7, 5],\n [12, 7, -10, -8],\n [12, -3, -5, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 325 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, -3, 12, -8],\n [0, -12, 1, -1],\n [0, 0, -5, 11],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 840 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-10, 0, -10, 0],\n [1, 3, -6, -6],\n [-9, 9, 3, 6],\n [-3, -12, -12, 8]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 200 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, -5, -9, -3],\n [0, 9, 8, 11],\n [0, 0, 7, 1],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 804 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, 10, -5, 7],\n [0, -5, 7, -9],\n [0, 0, -9, 11],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 680 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, 3, 11, -3],\n [6, -1, 11, 2],\n [-5, 1, -2, 2],\n [7, 1, 4, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 165 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, -11, 12, 5],\n [0, 4, 2, -9],\n [0, 0, 7, -2],\n [0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 320 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, 5, -10, 0],\n [0, -11, 0, -4],\n [0, 0, 3, 12],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 967 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[10, 8, 6, -7],\n [-8, -9, -3, 2],\n [-8, 4, 9, 2],\n [2, 7, -12, 0]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 746 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-4, -12, -11, -3],\n [11, 3, 4, 3],\n [-2, -1, 8, 2],\n [2, -3, 12, 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"
}
] | 649 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-4, 1, -3, 10],\n [1, 4, -10, -3],\n [-3, -10, 9, -6],\n [10, -3, -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"
}
] | 755 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-10, -6, -2, 9],\n [0, -12, 7, 6],\n [0, 0, -11, -1],\n [0, 0, 0, 8]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 440 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-7, -2, -4, 0],\n [-2, -6, -4, 0],\n [-4, -4, -5, 5],\n [0, 0, 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"
}
] | 234 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[1, 7, 5, 3],\n [12, 12, 8, -10],\n [12, 1, -5, -11],\n [0, 4, 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"
}
] | 268 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, 9, 6, 5],\n [0, 2, 10, -3],\n [0, 0, 11, -1],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 330 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[10, 0, 9, -1],\n [0, -6, 2, 2],\n [9, 2, 4, -11],\n [-1, 2, -11, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 898 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, -2, -4, 4],\n [-2, -1, -3, 10],\n [-4, -3, -7, 3],\n [4, 10, 3, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 937 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-8, 3, -4, -9],\n [0, 9, -12, -4],\n [0, 0, -1, 8],\n [0, 0, 0, -10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 280 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, -2, -10, 4],\n [-2, 2, 5, -6],\n [-10, 5, -9, -4],\n [4, -6, -4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 480 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[3, 6, 0, 1],\n [6, 4, 0, 4],\n [0, 0, -12, 7],\n [1, 4, 7, 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"
}
] | 512 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, -5, -6, -3],\n [-5, -9, -2, -3],\n [-6, -2, -4, -2],\n [-3, -3, -2, 3]]\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[[4, -4, -5, -6],\n [-4, 2, 4, -1],\n [-5, 4, -10, 2],\n [-6, -1, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 237 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, 0, 4, 6],\n [0, -5, -11, -12],\n [0, 0, 5, 11],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 875 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[8, -5, 0, -7],\n [8, 3, 0, 8],\n [-9, -5, -2, 4],\n [1, -3, 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"
}
] | 510 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-12, -4, 0, 7],\n [-4, -6, -2, -10],\n [0, -2, 8, 8],\n [7, -10, 8, 6]]\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": "Compute |A| for the matrix A =\n[[0, -5, -3, -8],\n [-5, 1, -3, 2],\n [-3, -3, 9, 9],\n [-8, 2, 9, 2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 193 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-12, 12, -5, 12],\n [0, -2, -10, -6],\n [0, 0, 6, -12],\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"
}
] | 576 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, 1, 8, 3],\n [-4, -11, 5, -1],\n [0, 3, -3, 0],\n [-2, 4, -10, 6]]\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[[-6, -10, 8, 8],\n [9, -6, 1, -11],\n [9, -5, -4, 0],\n [-9, 3, 8, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 896 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, 10, 6, 8],\n [0, 7, -1, 3],\n [0, 0, -7, -12],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 824 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-5, 8, -10, 4],\n [0, 11, -11, 2],\n [0, 0, -2, -9],\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"
}
] | 330 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[9, -1, 3, -7],\n [12, -6, 2, 0],\n [-2, -11, -8, -10],\n [4, -11, -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"
}
] | 134 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-12, 8, -4, 4],\n [8, -5, 0, -9],\n [-4, 0, 10, -2],\n [4, -9, -2, 0]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 904 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, -4, -6, -2],\n [-4, 6, 5, -2],\n [-6, 5, -12, 3],\n [-2, -2, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 203 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, 10, -6, 6],\n [10, -2, -2, -8],\n [-6, -2, -11, 8],\n [6, -8, 8, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 804 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-9, 1, -2, -4],\n [1, -11, -6, 4],\n [-2, -6, 4, 10],\n [-4, 4, 10, -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"
}
] | 696 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[2, -2, 0, -8],\n [0, 1, 4, -12],\n [12, 8, -11, 12],\n [4, 7, -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"
}
] | 10 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[10, 4, 2, 8],\n [4, 5, 8, -2],\n [2, 8, 6, -4],\n [8, -2, -4, 12]]? 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": "What is the determinant of the matrix:\n[[0, -4, 0, -2],\n [-4, -2, -4, -6],\n [0, -4, -2, 0],\n [-2, -6, 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"
}
] | 16 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, 7, -2, -11],\n [0, 12, -12, 1],\n [0, 0, -2, -12],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 760 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-12, 1, 2, 6],\n [4, -5, -4, 5],\n [5, -7, -4, -6],\n [10, 1, 3, -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"
}
] | 665 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[5, 11, 2, -5],\n [0, -9, 5, 3],\n [0, 0, -10, 10],\n [0, 0, 0, 10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 500 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-1, -9, 9, -12],\n [2, -8, 5, 11],\n [-9, 10, -4, -10],\n [8, -10, -6, 8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 424 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[10, 2, 8, -3],\n [0, 12, 7, -10],\n [0, 0, -9, 4],\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"
}
] | 880 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-1, 1, -10, 1],\n [0, -9, -11, 10],\n [0, 0, -2, -6],\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"
}
] | 216 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[2, -12, 2, -12],\n [0, 11, -11, -11],\n [0, 0, -10, -3],\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"
}
] | 460 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-3, -11, 1, 10],\n [-5, 10, -1, -3],\n [0, -10, -8, 9],\n [-8, -5, 1, -12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 559 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[3, -4, 4, -5],\n [-8, 2, -1, 2],\n [4, -11, 9, 9],\n [-8, 2, 5, 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"
}
] | 876 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-5, -10, -2, 0],\n [-10, 12, 0, 6],\n [-2, 0, 4, -4],\n [0, 6, -4, -4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 136 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-10, 8, 3, -2],\n [8, 5, 7, -1],\n [3, 7, -10, 4],\n [-2, -1, 4, 8]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 501 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-4, 0, 12, 10],\n [0, 2, -12, 2],\n [0, 0, -1, 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"
}
] | 912 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[10, 6, -4, 0],\n [-10, 7, -10, -11],\n [1, 5, -6, 1],\n [-2, 2, -12, 8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 544 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[2, 9, 4, 12],\n [0, -11, -4, -3],\n [0, 0, 5, -2],\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"
}
] | 670 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-10, 9, -1, -12],\n [0, -10, 11, 5],\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"
}
] | 800 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[6, -10, -11, 3],\n [12, 12, -10, -1],\n [-3, -1, 2, 3],\n [4, 2, 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"
}
] | 74 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-10, -12, 12, 3],\n [12, -4, -12, 2],\n [-10, 12, -4, 0],\n [3, -1, -6, -9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 872 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-5, -5, 3, 4],\n [2, 11, -12, -4],\n [-4, 9, 7, -5],\n [3, 0, -3, 12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 660 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[6, -8, -9, -4],\n [0, -10, -11, -7],\n [0, 0, 12, 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"
}
] | 880 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, 7, 9, 4],\n [5, 7, 11, -11],\n [-6, -6, -11, -1],\n [-3, 11, 11, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 134 | MATH |
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