messages
listlengths 1
1
| ground_truth
stringclasses 992
values | dataset
stringclasses 1
value |
|---|---|---|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, 12, 5, 2],\n [12, 4, -2, -6],\n [5, -2, 12, -2],\n [2, -6, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
908
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, 2, -2, 8],\n [2, 4, 2, -8],\n [-2, 2, -2, 1],\n [8, -8, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
632
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-11, -8, 9, 11],\n [2, -3, -6, -12],\n [2, 12, -2, 0],\n [2, -5, 9, 0]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
370
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, -6, -12, -8],\n [0, -10, 0, 6],\n [0, 0, 5, 12],\n [0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
200
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[10, -1, -1, 8],\n [-1, 12, 5, 2],\n [-1, 5, 7, 0],\n [8, 2, 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"
}
] |
912
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[8, 1, 3, 10],\n [1, -4, 2, 6],\n [3, 2, 3, -2],\n [10, 6, -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"
}
] |
495
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-1, -7, -9, -8],\n [9, 3, 0, 8],\n [-5, -4, 7, -11],\n [-3, -2, 10, -11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
344
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-8, -4, 4, -4],\n [0, -5, 10, -5],\n [0, 0, -2, 11],\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"
}
] |
40
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-1, -8, 10, -2],\n [-8, 8, 10, 0],\n [10, 10, 1, 6],\n [-2, 0, 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"
}
] |
144
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[10, -9, -4, -10],\n [-4, 2, -4, -1],\n [0, 8, 0, 1],\n [7, 4, 10, 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"
}
] |
644
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[11, -3, 7, 7],\n [0, -4, -12, 10],\n [0, 0, 7, -2],\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"
}
] |
156
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-10, -6, 1, -1],\n [-6, -10, 9, -12],\n [1, 9, -10, 4],\n [-1, -12, 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"
}
] |
349
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[1, 2, 4, 4],\n [2, -10, 1, 6],\n [4, 1, -4, 2],\n [4, 6, 2, -8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
888
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, -10, 8, -3],\n [0, 9, -6, 5],\n [2, -10, 8, -4],\n [-10, -6, -9, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
780
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, 1, 4, 0],\n [1, -1, 4, -8],\n [4, 4, 9, 8],\n [0, -8, 8, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
414
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, 11, 12, 9],\n [-2, 2, 10, -1],\n [-3, 6, -6, 8],\n [-9, -1, -11, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
221
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, -9, 2, -5],\n [12, -6, 12, 1],\n [-2, 11, -12, -4],\n [0, 11, 12, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
956
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, 0, 6, -11],\n [0, 9, 11, 6],\n [0, 0, -9, -10],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
430
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, -2, 12, -9],\n [-5, 12, 8, -5],\n [4, -4, -9, -6],\n [4, 11, 1, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
372
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-5, 8, -1, -2],\n [8, 11, -5, -4],\n [-1, -5, -3, 10],\n [-2, -4, 10, 8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
52
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[11, 0, -4, 6],\n [0, -8, 4, 0],\n [-4, 4, -2, -4],\n [6, 0, -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"
}
] |
256
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, -5, 5, 11],\n [0, -6, 11, 6],\n [0, 0, -2, -10],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
964
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[10, -2, 0, 11],\n [-12, 2, -11, -10],\n [-12, -2, -4, -4],\n [3, 8, -8, -4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
646
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-9, -2, 7, 1],\n [-5, -1, -11, 11],\n [-9, 8, 10, 0],\n [11, -7, -1, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
479
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[3, -2, 2, -6],\n [-2, 2, -8, 0],\n [2, -8, 12, -3],\n [-6, 0, -3, 3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
654
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[6, 12, -11, -4],\n [1, -12, 4, -9],\n [6, 5, -11, 4],\n [3, 8, 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"
}
] |
94
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, 5, 7, -10],\n [0, -10, 3, -9],\n [0, 0, 12, 9],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
640
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-10, 6, 4, 12],\n [6, 8, -1, 0],\n [4, -1, -4, -2],\n [12, 0, -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"
}
] |
584
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-9, -8, 6, -4],\n [-8, 9, 5, 4],\n [6, 5, -12, 1],\n [-4, 4, 1, 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"
}
] |
603
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, -6, 12, 9],\n [0, -9, 1, 7],\n [0, 0, 5, 1],\n [0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
975
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-9, 9, 1, 8],\n [0, 10, -4, -9],\n [0, 0, -6, 0],\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"
}
] |
680
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 8, 4, 3],\n [1, -12, 9, 3],\n [12, 5, -4, 2],\n [1, 8, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
88
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[4, -7, -5, 0],\n [9, 12, 9, -6],\n [9, -3, -12, -8],\n [-11, 1, 1, 8]]? 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": "Determine the value of det(A) where A =\n[[-6, -12, 9, 0],\n [4, -2, -12, 2],\n [-12, 10, -4, -7],\n [5, 9, -1, -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"
}
] |
402
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, -10, -10, -4],\n [0, 9, -5, -2],\n [0, 0, 2, 7],\n [0, 0, 0, 2]]\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[[-4, 8, 7, 9],\n [11, 11, -2, -5],\n [-9, -2, 11, -9],\n [-10, -3, -10, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
917
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, -8, 2, 12],\n [0, 6, -3, -11],\n [0, 0, 3, -2],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
990
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[7, -1, -12, 3],\n [-2, -5, -8, 7],\n [1, 12, 7, 12],\n [9, 4, 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"
}
] |
685
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, -6, -2, -3],\n [-6, 10, 3, 6],\n [-2, 3, 1, -2],\n [-3, 6, -2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
979
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-2, 4, 8, -4],\n [4, 3, -8, -6],\n [8, -8, -8, -9],\n [-4, -6, -9, 11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
358
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[12, 7, 11, -7],\n [12, -2, -7, 7],\n [-7, -10, 3, -8],\n [2, 5, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
302
|
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 [-9, -6, -9, -5],\n [1, -10, 4, -9],\n [-10, -2, 7, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
381
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, -3, 0, 2],\n [-3, 9, -8, -8],\n [0, -8, -1, -11],\n [2, -8, -11, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
572
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, -3, 7, 0],\n [5, -12, 1, 6],\n [-10, 11, -10, -7],\n [2, 6, 10, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
55
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, 0, 12, 4],\n [0, 8, 0, 8],\n [12, 0, -2, 5],\n [4, 8, 5, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
216
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-10, -7, 4, -4],\n [-2, -5, 5, -8],\n [9, 9, -10, -4],\n [4, -11, 11, -5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
905
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-6, -11, 2, -8],\n [0, -4, -11, -1],\n [0, 0, -1, 9],\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"
}
] |
856
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[11, 8, 1, -8],\n [8, -9, -6, 4],\n [1, -6, 11, -4],\n [-8, 4, -4, 5]]\nRound to the nearest integer, then take the result modulo 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, 0, 3, 4],\n [0, 7, -4, 4],\n [3, -4, 8, -4],\n [4, 4, -4, -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"
}
] |
63
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-9, -3, 4, -3],\n [-3, 9, 2, 8],\n [4, 2, 7, -9],\n [-3, 8, -9, -3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
697
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, -1, 8, 0],\n [0, -4, 0, -4],\n [0, 0, 1, -9],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
904
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-8, -7, -11, 11],\n [0, 1, -12, 10],\n [0, 0, -4, 10],\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"
}
] |
776
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-1, -2, 0, -2],\n [-6, -1, 1, 10],\n [-1, -9, -5, 7],\n [2, -6, -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"
}
] |
321
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, -6, -7, 4],\n [-6, -1, 7, -2],\n [-7, 7, -1, 0],\n [4, -2, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
65
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-8, 2, 2, 6],\n [2, 6, 5, 1],\n [2, 5, -4, -6],\n [6, 1, -6, -4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
80
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-4, 0, 2, 1],\n [0, -6, 9, -6],\n [2, 9, 7, 2],\n [1, -6, 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"
}
] |
567
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[1, 2, 6, -8],\n [2, 9, -6, 7],\n [6, -6, 1, 2],\n [-8, 7, 2, 4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
555
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-6, -5, 4, -9],\n [-10, 9, 4, 1],\n [0, -2, 1, -1],\n [-1, 0, -10, 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"
}
] |
948
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, -6, -12, -6],\n [3, -4, 7, 11],\n [-8, 7, 0, -9],\n [-8, -11, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
353
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[11, -10, 11, -1],\n [0, -9, 3, 8],\n [0, 0, 1, 9],\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"
}
] |
109
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 2, -2, 0],\n [2, 11, 8, -3],\n [-2, 8, 10, 3],\n [0, -3, 3, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
991
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, 3, -6, -7],\n [0, 9, 10, 8],\n [0, 0, -10, -10],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
700
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, -1, 4, 2],\n [-1, 6, -1, -3],\n [4, -1, -10, 6],\n [2, -3, 6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
416
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-6, 9, 2, 0],\n [9, 3, 2, 8],\n [2, 2, 8, -4],\n [0, 8, -4, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
248
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-3, -10, 4, 11],\n [0, 5, 3, 4],\n [0, 0, -5, 9],\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"
}
] |
450
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[9, -2, -4, -2],\n [-2, 11, 1, 0],\n [-4, 1, -5, -8],\n [-2, 0, -8, -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"
}
] |
732
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[6, 5, 4, -12],\n [-3, -6, -10, 7],\n [-3, -5, -9, 11],\n [-8, -6, -5, -5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
331
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[8, 11, -5, -6],\n [0, -6, 8, 8],\n [0, 0, 12, 12],\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"
}
] |
184
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 0, 1, -8],\n [0, -5, 8, 2],\n [1, 8, 2, 6],\n [-8, 2, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
537
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, -2, -2, -6],\n [-2, -10, -2, -5],\n [-2, -2, 3, -8],\n [-6, -5, -8, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
987
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-4, -11, -2, -11],\n [0, -1, 5, 3],\n [0, 0, 10, 9],\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"
}
] |
320
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[6, 10, -6, 2],\n [12, 5, 4, -12],\n [-6, -6, -11, -2],\n [-1, -12, 4, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
802
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, -5, -5, -4],\n [-4, 2, 6, 1],\n [3, -12, -9, 7],\n [-3, -11, -10, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
299
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-6, -8, 8, 6],\n [-10, 11, -1, 10],\n [-7, 12, 12, 1],\n [6, 10, 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"
}
] |
188
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-5, -1, 6, -10],\n [-1, -6, 0, -4],\n [6, 0, 5, 0],\n [-10, -4, 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"
}
] |
410
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, 1, 11, -4],\n [1, -11, 1, 3],\n [11, -7, 8, -7],\n [6, 0, -2, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
374
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, -1, 6, -6],\n [5, 4, -5, 10],\n [-7, -12, -1, 2],\n [-10, 12, 2, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
184
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, -4, -10, 5],\n [-4, -1, 1, 0],\n [-10, 1, -10, 2],\n [5, 0, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
951
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, -6, 1, -10],\n [0, -5, 11, 0],\n [0, 0, 2, 12],\n [0, 0, 0, 7]]\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[[0, 11, 4, 5],\n [5, -8, 3, 10],\n [-11, 10, -7, 5],\n [7, -2, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
255
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, -11, 9, 4],\n [-11, 0, 2, 1],\n [9, 2, -10, -2],\n [4, 1, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
19
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[5, 2, 0, -5],\n [11, -2, 5, 7],\n [-2, -10, -2, -6],\n [6, -10, -10, 3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
734
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, 3, -1, -12],\n [0, 3, -2, 3],\n [0, 0, 12, -5],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
360
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[1, 1, 9, 8],\n [0, -12, -12, -4],\n [0, 0, -8, -10],\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"
}
] |
768
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[9, -9, 1, -9],\n [0, -1, -10, -7],\n [0, 0, -7, -9],\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"
}
] |
244
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-1, 2, 6, -9],\n [8, -2, -1, 12],\n [-5, 1, 8, -6],\n [-1, -3, -11, 8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
508
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-3, 1, 7, 8],\n [1, 11, -8, -2],\n [7, -8, 3, 6],\n [8, -2, 6, -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"
}
] |
987
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[3, -4, 6, 2],\n [-6, 10, -6, 2],\n [-9, 4, 12, 10],\n [-3, -8, -1, 1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
796
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[5, 7, -1, -4],\n [3, -9, -9, 12],\n [0, -5, 12, 12],\n [-12, 5, -11, 7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
994
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[12, -6, 8, -8],\n [-4, 11, -1, 9],\n [7, 9, -3, 4],\n [-8, -5, -9, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
738
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 0, 0, 2],\n [0, -5, 10, -4],\n [0, 10, 5, -7],\n [2, -4, -7, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
400
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[11, 8, -1, 12],\n [3, -7, -8, 6],\n [2, -3, 1, -3],\n [-11, 6, 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"
}
] |
861
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, -1, -7, 2],\n [0, -6, -8, -12],\n [0, 0, 2, 8],\n [0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
56
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, 4, 6, 5],\n [4, 5, 1, -9],\n [6, 1, -10, -5],\n [5, -9, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
346
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, 5, 7, 6],\n [4, -6, 1, 2],\n [-8, 11, -11, 6],\n [-9, -3, -10, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
916
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[4, 8, -6, 5],\n [8, 7, 3, 0],\n [-6, 3, -6, -4],\n [5, 0, -4, 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"
}
] |
251
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[10, -7, 0, 5],\n [0, -10, 4, 7],\n [0, 0, 3, -8],\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"
}
] |
100
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, 0, 2, 11],\n [0, 10, -8, 9],\n [0, 0, -12, 10],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
720
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[1, 5, -11, -7],\n [0, 1, 2, 5],\n [0, 0, -1, -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"
}
] |
3
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[4, -2, -7, -1],\n [0, 5, -5, 6],\n [0, 0, -6, 2],\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"
}
] |
240
|
MATH
|
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