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[[1, -8, 7, -7],\n [0, -10, -7, 10],\n [0, 0, 5, 10],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
450
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[12, -11, 7, -12],\n [0, 11, 1, -12],\n [0, 0, -6, 9],\n [0, 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"
}
] |
40
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-2, 2, 9, 2],\n [2, -12, 4, 6],\n [9, 4, -6, -4],\n [2, 6, -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"
}
] |
32
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[9, 11, -3, 12],\n [0, -1, 2, -7],\n [0, 0, 8, -7],\n [0, 0, 0, -9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
648
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, -2, -12, 2],\n [-2, -1, 5, -2],\n [-12, 5, 10, -4],\n [2, -2, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
816
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, 6, -10, -4],\n [6, -1, -5, -2],\n [-10, -5, 10, 0],\n [-4, -2, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
320
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-8, 12, -7, -7],\n [0, -2, -9, 2],\n [0, 0, 8, -12],\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"
}
] |
872
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-1, -12, 1, -8],\n [0, 6, -9, 1],\n [0, 0, 8, 12],\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"
}
] |
576
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[3, -10, 10, 11],\n [-10, 10, -6, -4],\n [10, -6, -2, -5],\n [11, -4, -5, 0]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
62
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-1, -6, -5, 0],\n [-6, -3, 1, -3],\n [-5, 1, 8, -4],\n [0, -3, -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"
}
] |
313
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, 2, -10, 9],\n [0, 12, -8, 0],\n [0, 0, 8, 12],\n [0, 0, 0, -1]]\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[[10, -7, 9, -6],\n [6, 7, 2, -2],\n [2, -8, 2, 11],\n [-10, 7, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
908
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[4, 0, 12, -8],\n [0, 8, -3, -12],\n [0, 0, -12, -5],\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"
}
] |
304
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[0, 6, 0, 1],\n [6, -1, -6, 10],\n [0, -6, 3, -4],\n [1, 10, -4, -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"
}
] |
903
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[10, 7, 1, -10],\n [5, -5, 1, -9],\n [-4, -7, 8, 0],\n [10, 11, 10, 0]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
786
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-11, 1, -11, 11],\n [0, -5, -8, 9],\n [0, 0, 2, 11],\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"
}
] |
210
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, -1, -12, 9],\n [3, 4, -6, -7],\n [-11, -1, -7, -5],\n [-3, 8, 7, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
243
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-11, 4, -2, 2],\n [4, 2, -6, 10],\n [-2, -6, -9, 7],\n [2, 10, 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"
}
] |
100
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-2, -10, -2, -2],\n [-10, -6, -5, -4],\n [-2, -5, -8, -2],\n [-2, -4, -2, 10]]\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": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, 2, 9, -7],\n [0, -2, -10, 0],\n [0, 0, 7, 11],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
210
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, 9, 6, 6],\n [-1, 9, -4, 11],\n [3, -4, 1, 9],\n [-3, 6, 5, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
320
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, -11, 12, -3],\n [0, 8, -10, 1],\n [0, 0, 10, -1],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
400
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[1, -7, 12, 3],\n [0, 10, 8, -6],\n [0, 0, 6, 1],\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"
}
] |
820
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, -1, 0, -6],\n [-1, 1, -2, -10],\n [0, -2, -6, 0],\n [-6, -10, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
422
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, -10, -2, -4],\n [-10, 3, -3, 6],\n [-2, -3, 1, 0],\n [-4, 6, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
644
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-1, 1, 10, 5],\n [0, -2, 2, -6],\n [0, 0, 3, -12],\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"
}
] |
994
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-6, 5, 0, 11],\n [10, 8, -8, 5],\n [-12, -12, 5, 12],\n [7, -9, 2, -11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
541
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[1, -4, -4, 12],\n [-4, 10, 8, -2],\n [-4, 8, -12, -10],\n [12, -2, -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"
}
] |
656
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[7, -5, 6, -6],\n [10, -5, 1, 8],\n [6, 7, 6, 8],\n [-10, 5, -5, -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"
}
] |
218
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-11, 4, -12, 3],\n [-10, -7, 1, 10],\n [6, -2, 10, -9],\n [-7, 8, 12, -8]]\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": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, -5, 2, -1],\n [-5, -11, 4, 2],\n [2, 4, -8, -4],\n [-1, 2, -4, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
872
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[4, 1, -8, 2],\n [1, 7, 8, 0],\n [-8, 8, 3, 8],\n [2, 0, 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"
}
] |
384
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[5, 5, -1, 2],\n [5, 8, 1, 2],\n [-1, 1, 2, 0],\n [2, 2, 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"
}
] |
936
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[6, 4, 8, -6],\n [4, -3, 0, 2],\n [8, 0, -10, -9],\n [-6, 2, -9, 9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
478
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, 2, -8, -4],\n [2, -7, -10, 4],\n [-8, -10, 0, 4],\n [-4, 4, 4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
408
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, 10, -5, -4],\n [7, 9, 0, 5],\n [1, 1, -6, -10],\n [-9, -11, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
878
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, 9, 2, -6],\n [9, -6, 6, 9],\n [2, 6, 5, -4],\n [-6, 9, -4, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
555
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, 5, -8, -6],\n [-6, -11, 1, 11],\n [6, 1, 11, -12],\n [-7, 8, 8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
789
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, -2, -7, -2],\n [-2, 12, -2, 0],\n [-7, -2, 5, 9],\n [-2, 0, 9, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
904
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-2, -6, -8, 0],\n [-6, -10, -8, 2],\n [-8, -8, 9, 5],\n [0, 2, 5, 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"
}
] |
88
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[7, 12, 0, 0],\n [12, 2, -8, 8],\n [0, -8, 11, -6],\n [0, 8, -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"
}
] |
396
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-10, 5, 7, 1],\n [5, 12, 0, 8],\n [7, 0, 12, 8],\n [1, 8, 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"
}
] |
120
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[4, 2, 7, 10],\n [2, -8, -2, 8],\n [7, -2, 0, -2],\n [10, 8, -2, 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"
}
] |
24
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-1, -6, -4, 6],\n [-6, -5, 5, -10],\n [-4, 5, 11, 3],\n [6, -10, 3, 1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
923
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 5, 7, 1],\n [5, -2, -4, -2],\n [7, -4, 9, 0],\n [1, -2, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
741
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-1, 0, 3, -5],\n [10, -12, 4, 7],\n [-5, -12, 10, 9],\n [3, -7, 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"
}
] |
315
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, 1, -4, 2],\n [1, 7, 8, -3],\n [-4, 8, -2, 5],\n [2, -3, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
532
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[5, 1, 4, -1],\n [0, 1, -10, 0],\n [0, 0, 7, 4],\n [0, 0, 0, -2]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
930
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-3, 3, -7, -4],\n [0, -2, 5, 0],\n [0, 0, -10, 11],\n [0, 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"
}
] |
700
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, -11, -12, 0],\n [-5, -4, -11, 7],\n [5, -3, 1, 10],\n [10, 9, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
41
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[5, 0, -1, -4],\n [0, -8, -6, 10],\n [-4, 11, 10, -7],\n [-6, 4, 12, -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"
}
] |
252
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-4, -4, -6, 2],\n [-4, 10, 0, 2],\n [-6, 0, 8, -2],\n [2, 2, -2, -12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
288
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, -6, 1, -2],\n [0, -7, 1, -11],\n [-1, 8, 1, 5],\n [7, -5, -10, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
250
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[12, -5, -9, 6],\n [-4, 5, 10, 12],\n [-7, 12, 4, 8],\n [6, 3, -12, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
790
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, 4, 6, -12],\n [0, 10, -6, 3],\n [0, 0, 3, -6],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
530
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, -2, -6, 8],\n [-2, -12, 5, 4],\n [-6, 5, -5, 2],\n [8, 4, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
338
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, 2, -2, -3],\n [2, 2, 6, -2],\n [-2, 6, 0, 6],\n [-3, -2, 6, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
92
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[12, -11, -7, -3],\n [-6, 3, -11, -3],\n [5, -9, 2, -7],\n [8, 4, -11, -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"
}
] |
90
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-2, -2, 6, -6],\n [7, -11, -11, 4],\n [2, 2, -4, -12],\n [-7, 5, 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"
}
] |
904
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-3, 4, -7, 2],\n [0, 10, -4, -12],\n [0, 0, 5, -4],\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"
}
] |
200
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[5, 9, 12, -11],\n [2, -1, -2, 10],\n [10, -1, -5, 1],\n [3, 10, 7, 5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
419
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, -8, -1, -5],\n [0, 9, -7, 12],\n [0, 0, -12, -6],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
488
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[12, 6, -11, 12],\n [6, -5, -10, -8],\n [11, 0, -8, -7],\n [-3, 3, -6, -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"
}
] |
463
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[0, 11, 10, -6],\n [-2, -7, -2, 8],\n [-6, -8, -1, 5],\n [7, -2, -4, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
448
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, 0, -6, 6],\n [0, 9, -3, 0],\n [-6, -3, 7, -9],\n [6, 0, -9, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
324
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[11, -5, 2, -5],\n [-5, -6, 0, 6],\n [2, 0, 5, 6],\n [-5, 6, 6, 2]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
268
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[6, 2, -4, 11],\n [0, -11, 5, 0],\n [0, 0, -5, 1],\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"
}
] |
960
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-11, 10, -1, -1],\n [10, 5, -5, -5],\n [-1, -5, -4, 4],\n [-1, -5, 4, -8]]? Round to the nearest integer, then express your answer modulo 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[[-10, 11, 2, 10],\n [-1, -4, 2, -4],\n [-5, 2, 12, -3],\n [4, 11, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
348
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-8, -4, -4, 6],\n [-4, 8, 11, 0],\n [-4, 11, 12, -3],\n [6, 0, -3, -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"
}
] |
100
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-7, -5, 1, 4],\n [-5, 5, -1, 4],\n [1, -1, -7, -2],\n [4, 4, -2, -11]]\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": "Determine the value of det(A) where A =\n[[2, -2, 9, -9],\n [8, 7, -12, 1],\n [7, 4, 2, -1],\n [-2, -2, 11, -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"
}
] |
711
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-6, 3, 4, -2],\n [3, 0, 6, -4],\n [4, 6, 11, 0],\n [-2, -4, 0, 0]]\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[[10, 9, 4, 2],\n [9, -2, -4, 2],\n [4, -4, 8, 0],\n [2, 2, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
112
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-1, -10, -7, -8],\n [-11, 9, -6, -3],\n [8, 0, 4, 3],\n [10, 11, 8, 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"
}
] |
739
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-10, 10, -11, 11],\n [8, 8, 11, -1],\n [1, 11, 3, -10],\n [-4, -1, 3, -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"
}
] |
272
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, 2, 5, -9],\n [-10, -2, -10, -9],\n [-11, 6, 12, -3],\n [2, -7, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
25
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-5, -8, 3, 0],\n [0, -11, 0, 11],\n [0, 0, -7, -4],\n [0, 0, 0, -12]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
620
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[5, 0, -6, 7],\n [0, -10, -8, -7],\n [0, 0, 1, -4],\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"
}
] |
400
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-5, -10, 2, 1],\n [0, -6, -5, 7],\n [0, 0, 4, 3],\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"
}
] |
640
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[2, 5, 3, 10],\n [0, 3, -11, 9],\n [0, 0, -11, 6],\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"
}
] |
528
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-1, 6, -8, -7],\n [6, 10, -1, -8],\n [-8, -1, 0, 2],\n [-7, -8, 2, 10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
507
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, 5, -7, 2],\n [2, 0, 6, -7],\n [-2, -8, -8, 10],\n [2, 5, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
282
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, -5, 4, 4],\n [-5, -8, -7, -3],\n [4, -7, 6, 2],\n [4, -3, 2, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
985
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-9, 5, 7, -2],\n [0, -6, 11, -2],\n [0, 0, -2, -7],\n [0, 0, 0, -4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
432
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, 8, -12, -7],\n [0, -6, 12, 5],\n [0, 0, 3, -12],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
218
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[12, 4, 5, -6],\n [0, 6, 6, -6],\n [0, 0, -10, 11],\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"
}
] |
840
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, 6, -2, 0],\n [6, 10, 1, 6],\n [-2, 1, 9, 4],\n [0, 6, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
476
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, 0, 6, -8],\n [0, 5, -6, 9],\n [6, -6, -5, 1],\n [-8, 9, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
172
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-10, 2, -2, -5],\n [-11, -10, 7, 11],\n [3, -11, -11, 1],\n [7, 9, 6, 0]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
49
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-5, 12, -12, 11],\n [0, -2, 4, 11],\n [-8, -9, -11, -1],\n [5, -11, -3, -11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
768
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-4, 5, 3, 9],\n [0, 7, -11, 12],\n [0, 0, 12, 8],\n [0, 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"
}
] |
680
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-3, 0, -2, 6],\n [0, -7, 3, -6],\n [-2, 3, 2, 4],\n [6, -6, 4, 7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
203
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, -9, -6, 9],\n [0, 10, -3, -1],\n [0, 0, -11, 6],\n [0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
700
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-5, 1, -7, 0],\n [0, -2, -1, 8],\n [0, 0, -6, -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"
}
] |
580
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, 6, 8, 1],\n [-5, 5, 12, 3],\n [2, 8, 4, -7],\n [-1, -3, 9, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
695
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, 1, 12, -12],\n [-1, -10, -6, -10],\n [3, 2, -7, 12],\n [0, -7, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
227
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-12, -6, 3, -3],\n [0, 1, 1, -2],\n [0, 0, 11, 3],\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"
}
] |
680
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 1, 8, 4],\n [0, -6, 9, -5],\n [0, 0, -8, -11],\n [0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
408
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, 9, -8, -12],\n [-7, 10, -10, -3],\n [-12, 7, 11, -12],\n [-8, -6, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
353
|
MATH
|
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