messages
listlengths 1
1
| ground_truth
stringclasses 992
values | dataset
stringclasses 1
value |
|---|---|---|
[
{
"content": "Compute |A| for the matrix A =\n[[-8, -1, -9, 11],\n [0, 10, -7, -7],\n [0, 0, 5, -4],\n [0, 0, 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"
}
] |
0
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[8, 5, 1, -3],\n [-12, 5, 6, 7],\n [0, 6, 11, 10],\n [12, 7, -5, 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"
}
] |
780
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[6, 4, -2, 0],\n [4, 7, 5, -2],\n [-2, 5, 4, 6],\n [0, -2, 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"
}
] |
840
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-4, 12, 7, -11],\n [0, -12, -8, -4],\n [0, 0, -12, -3],\n [0, 0, 0, 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"
}
] |
240
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[9, -3, -5, -12],\n [0, -6, 8, 4],\n [0, 0, -7, 7],\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"
}
] |
134
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-10, 0, 2, 8],\n [0, -4, -2, 6],\n [2, -2, -8, -1],\n [8, 6, -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"
}
] |
176
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, 1, 8, -10],\n [11, -8, 6, 7],\n [-9, -3, 7, -2],\n [-5, 1, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-1, -4, 8, 8],\n [9, 10, -12, -12],\n [-5, 8, 9, 7],\n [-9, -8, 12, 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"
}
] |
752
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, -8, 5, -4],\n [0, -9, -8, 4],\n [0, 0, 7, 1],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
118
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[6, 0, -6, 0],\n [0, 10, 8, -1],\n [-6, 8, 4, 8],\n [0, -1, 8, 1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
900
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[9, -1, -8, -10],\n [0, -1, -1, 6],\n [0, 0, 12, 12],\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"
}
] |
296
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, 10, 12, -2],\n [0, -2, -8, 9],\n [0, 0, -12, 7],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
432
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-5, 2, 10, -6],\n [2, 5, 6, 11],\n [10, 6, -6, -4],\n [-6, 11, -4, 11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
72
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[3, 7, -12, 1],\n [10, -9, 4, -10],\n [-1, 8, 6, 0],\n [-2, -6, -7, 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"
}
] |
279
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, -11, 7, 0],\n [0, 8, -10, -10],\n [0, 0, 9, -9],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
760
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[7, 8, -5, 1],\n [2, -9, -6, 11],\n [7, 4, 4, 7],\n [6, 2, -9, -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"
}
] |
949
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[12, 10, 6, -2],\n [0, 2, 3, -4],\n [0, 0, 5, -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"
}
] |
720
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 8, -12, -9],\n [0, -11, -7, -8],\n [10, -10, 12, -8],\n [2, 5, -12, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
590
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[6, -1, -10, -3],\n [0, 7, 11, -10],\n [0, 0, -2, -8],\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"
}
] |
504
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, -2, 4, -9],\n [-2, 4, 5, 12],\n [4, 5, -4, -5],\n [-9, 12, -5, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
513
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[12, -4, -2, 8],\n [-4, -10, 2, 0],\n [-2, 2, -2, 5],\n [8, 0, 5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
392
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[1, 4, 4, -5],\n [4, -12, 12, 3],\n [4, 12, -9, -10],\n [-5, 3, -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"
}
] |
557
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[6, 2, -8, 11],\n [0, -11, 5, -1],\n [0, 0, 5, -3],\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"
}
] |
330
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[10, -3, 4, -3],\n [-3, 9, 9, 6],\n [4, 9, -12, 10],\n [-3, 6, 10, -10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
377
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-8, 2, 1, -11],\n [12, -8, -8, 10],\n [-3, 0, -8, -1],\n [3, 0, -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"
}
] |
48
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-9, 3, -12, 0],\n [3, 9, -4, 2],\n [-12, -4, -1, -8],\n [0, 2, -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"
}
] |
996
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, -4, 1, 8],\n [0, 11, -4, -3],\n [0, 0, 8, 2],\n [0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
760
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[9, -6, -1, 0],\n [0, 11, 12, 1],\n [0, 0, 12, 9],\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"
}
] |
872
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[10, -1, -2, 0],\n [-1, 9, -2, -6],\n [-2, -2, 0, -2],\n [0, -6, -2, 7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
672
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-11, -12, 0, 8],\n [-10, -2, -6, 0],\n [7, -2, 3, 2],\n [-9, -5, 1, -3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
758
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-2, -7, 12, 4],\n [0, -3, 8, -2],\n [0, 0, -7, 9],\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"
}
] |
420
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[8, 7, -6, 0],\n [-11, -9, 10, 0],\n [-8, -8, 1, 11],\n [-1, 10, 9, -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"
}
] |
298
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, -5, 4, 5],\n [1, -3, 11, 8],\n [12, 1, -4, -7],\n [-12, 1, -2, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
436
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[5, 1, -1, 4],\n [1, -9, 11, -4],\n [-1, 11, -9, 3],\n [4, -4, 3, -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"
}
] |
354
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, 3, 12, -6],\n [-6, 1, 12, 5],\n [-11, 11, 9, -10],\n [8, -1, 9, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
73
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, -11, 3, 5],\n [3, 4, 2, 3],\n [9, -5, -4, 2],\n [0, 8, 11, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
25
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-10, 6, -6, -4],\n [6, -11, 2, 10],\n [-6, 2, -1, 4],\n [-4, 10, 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"
}
] |
286
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[9, 4, 7, -10],\n [0, 6, -12, -5],\n [0, 0, 2, -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"
}
] |
648
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[5, 6, 2, -2],\n [6, -8, 0, 2],\n [2, 0, -12, 2],\n [-2, 2, 2, -8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
232
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[9, 3, 1, 12],\n [0, 1, 9, 4],\n [0, 0, -4, 1],\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"
}
] |
856
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, -8, -4, 10],\n [-8, 4, -1, 4],\n [-4, -1, 1, 2],\n [10, 4, 2, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
864
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[1, 2, -6, -7],\n [0, -9, -9, -5],\n [0, 0, 1, -7],\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"
}
] |
955
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[2, 8, -4, 8],\n [6, -8, 11, 11],\n [-2, -2, -7, 0],\n [-11, 0, 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"
}
] |
804
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[10, -4, -3, -12],\n [0, 6, -5, 2],\n [0, 0, 12, -11],\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"
}
] |
360
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, 0, 1, 0],\n [0, -2, 4, -5],\n [1, 4, -12, 5],\n [0, -5, 5, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
751
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[12, 2, -6, -5],\n [-1, 11, -10, -5],\n [-2, -4, -6, 10],\n [-8, -11, 11, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
500
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[0, 1, 3, -7],\n [-3, 5, -7, 9],\n [11, -10, 10, 11],\n [-2, 2, 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"
}
] |
435
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-11, 5, 10, 1],\n [6, -8, -11, -9],\n [-7, 5, -10, 5],\n [10, -4, -3, 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"
}
] |
500
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-11, -8, 6, -2],\n [-11, 0, -11, 6],\n [2, 5, 6, -11],\n [-4, 0, -4, 1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
521
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, -10, 12, -9],\n [0, 9, 7, -9],\n [0, 0, -4, -4],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
248
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, 6, 12, 11],\n [8, -4, -3, -1],\n [11, 0, 2, 9],\n [10, 0, 10, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
914
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-4, 12, -5, -7],\n [0, -6, 5, 2],\n [0, 0, -7, 2],\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"
}
] |
336
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, 12, 0, 4],\n [0, -8, 11, -5],\n [0, 0, -4, -8],\n [0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
512
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[2, 0, 0, -2],\n [0, -6, -3, 1],\n [0, 0, 4, 6],\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"
}
] |
432
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, 7, 11, 11],\n [9, 12, -8, -6],\n [-10, 4, 8, 5],\n [-2, 12, 7, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
301
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, -2, 10, -11],\n [-6, -6, 4, -8],\n [11, 12, 12, 1],\n [8, 0, -5, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
532
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-4, 0, -2, -6],\n [0, 0, 0, -7],\n [-2, 0, -12, 1],\n [-6, -7, 1, 7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
844
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-4, 12, -8, 4],\n [0, 3, 8, -3],\n [0, 0, 3, 9],\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"
}
] |
360
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-12, -4, 0, -2],\n [-4, -6, 6, 5],\n [0, 6, 7, 6],\n [-2, 5, 6, -11]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
996
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-9, 0, 8, 4],\n [0, -9, 3, 0],\n [8, 3, -5, 2],\n [4, 0, 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"
}
] |
192
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, 7, -8, 9],\n [7, 6, 1, -8],\n [-8, 1, 1, 0],\n [9, -8, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
564
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, 6, 11, 2],\n [-4, -8, 12, -9],\n [1, 6, 5, 7],\n [-7, -4, 9, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
264
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, -6, -4, 0],\n [-6, 11, 0, 9],\n [-4, 0, 11, -3],\n [0, 9, -3, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
560
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, 9, 9, -6],\n [-7, 0, -6, -11],\n [-6, -10, 2, 1],\n [5, 11, -11, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
414
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[5, -1, 8, 10],\n [0, -3, -9, 5],\n [0, 0, 4, -10],\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"
}
] |
880
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, 11, 12, 11],\n [0, -6, -10, 10],\n [0, 0, 12, 9],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
800
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[11, 6, -1, 4],\n [6, 12, 3, 8],\n [-1, 3, -6, -5],\n [4, 8, -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"
}
] |
476
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[4, 11, 7, 4],\n [0, -11, 9, -11],\n [0, 0, 2, -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"
}
] |
616
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-5, 4, -8, -8],\n [4, 11, -1, 4],\n [-8, -1, -4, 4],\n [-8, 4, 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"
}
] |
306
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, 1, 2, -4],\n [1, 4, 2, 1],\n [2, 2, -10, -8],\n [-4, 1, -8, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
400
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, -11, 3, 2],\n [-12, -5, 4, -9],\n [7, -11, 1, 6],\n [-12, -8, -7, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
66
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-7, -6, 5, 3],\n [0, 11, 6, -9],\n [0, 0, 12, 2],\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"
}
] |
380
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[4, -6, 3, -1],\n [-6, 4, -9, -11],\n [3, -9, 11, 8],\n [-1, -11, 8, 6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
528
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, 8, -3, -10],\n [0, 12, -2, 12],\n [0, 0, -6, -2],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
128
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-12, 2, -2, 1],\n [2, -7, 11, 6],\n [-2, 11, 6, -4],\n [1, 6, -4, 0]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
235
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-9, -3, 8, 4],\n [-4, 12, 1, -2],\n [10, 4, -8, -4],\n [-11, -9, -8, 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"
}
] |
376
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, 7, 2, -11],\n [10, -12, 7, -7],\n [2, -9, 8, 12],\n [3, 9, -2, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
111
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[9, -4, -12, -4],\n [11, -9, 11, 7],\n [-5, 12, -8, 2],\n [-9, -2, -3, -2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
618
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-2, -5, 6, 4],\n [-5, 7, -2, 0],\n [6, -2, 3, 10],\n [4, 0, 10, -1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
429
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, 2, 2, 5],\n [2, 5, 4, 10],\n [2, 4, -9, -4],\n [5, 10, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
869
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-10, -5, 12, -1],\n [0, -4, -9, 5],\n [0, 0, 9, 6],\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"
}
] |
40
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, -10, -8, -11],\n [0, -9, -4, 5],\n [0, 0, 11, 3],\n [0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
960
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, -3, 2, 2],\n [-3, 10, -6, 8],\n [2, -6, 9, -6],\n [2, 8, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
910
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-10, 4, 5, 1],\n [4, -4, 2, 0],\n [5, 2, 8, 2],\n [1, 0, 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"
}
] |
948
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[1, 6, -8, -12],\n [-9, 12, -11, -3],\n [6, -5, -9, 12],\n [-12, -5, 9, 7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
883
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, 11, 5, 3],\n [0, 1, -1, 7],\n [0, 0, -3, 7],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
976
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, 11, 3, -4],\n [0, 11, -1, -9],\n [0, 0, -3, -2],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
848
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-5, -10, -4, -9],\n [7, 8, 4, 6],\n [-11, -10, -7, -6],\n [-4, -10, -12, 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"
}
] |
670
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-1, 10, 4, 10],\n [10, 10, 6, 8],\n [4, 6, 7, 11],\n [10, 8, 11, -9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
972
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, 6, -5, 7],\n [0, 5, 3, -7],\n [0, 0, 10, -4],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
400
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, 0, 7, 2],\n [0, -9, -10, -6],\n [7, -10, 9, 4],\n [2, -6, 4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
68
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, -4, -3, -6],\n [-4, 11, -6, 0],\n [-3, -6, -10, 0],\n [-6, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
26
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, 8, -3, -2],\n [0, 1, 6, 10],\n [0, 0, -8, -8],\n [0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
360
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, -8, 7, -2],\n [0, -10, -8, 7],\n [0, 0, -6, -1],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
360
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-11, -3, -8, -7],\n [0, 9, -12, 1],\n [0, 0, 12, -6],\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"
}
] |
120
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, -2, -8, -8],\n [0, -6, -12, 10],\n [0, 0, -8, 2],\n [0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
960
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[12, 11, 3, -6],\n [6, -4, -3, -1],\n [3, 2, 10, 1],\n [8, 8, 1, -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"
}
] |
400
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, 11, 9, 3],\n [0, 11, -10, 9],\n [0, 0, -9, 1],\n [0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
515
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-7, 7, -1, 0],\n [7, 12, 7, -12],\n [-1, 7, -6, -6],\n [0, -12, -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"
}
] |
712
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, -2, -8, 0],\n [0, 10, 6, 12],\n [0, 0, 2, -9],\n [0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
360
|
MATH
|
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