messages
listlengths 1
1
| ground_truth
stringclasses 992
values | dataset
stringclasses 1
value |
|---|---|---|
[
{
"content": "Determine the value of det(A) where A =\n[[-6, -1, 4, -10],\n [-7, 5, 12, 3],\n [9, 11, 12, 1],\n [7, -7, -12, -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"
}
] |
344
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, 7, -3, 2],\n [7, -12, 2, 0],\n [-3, 2, -3, 0],\n [2, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
274
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, 11, -12, -1],\n [0, -7, 12, 11],\n [0, 0, -10, 8],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
520
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-5, 2, 8, -4],\n [2, 10, 5, -2],\n [8, 5, 7, -2],\n [-4, -2, -2, -9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
865
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-6, 3, -6, -3],\n [3, -8, 2, 2],\n [-6, 2, -10, 4],\n [-3, 2, 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"
}
] |
450
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, -2, -9, 7],\n [0, -3, 8, 7],\n [0, 0, 9, 3],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
432
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-6, 1, 5, -11],\n [0, 6, 2, -4],\n [0, 0, 6, -8],\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"
}
] |
864
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[12, -6, 2, 2],\n [-6, -9, 0, 6],\n [2, 0, -6, 3],\n [2, 6, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
596
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-7, 6, -6, -5],\n [0, 2, -9, 10],\n [0, 0, 10, 11],\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"
}
] |
300
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[12, -8, 7, -9],\n [-8, 10, -6, -6],\n [7, -6, -4, 4],\n [-9, -6, 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"
}
] |
142
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, -10, -8, 11],\n [-2, 1, -9, 11],\n [10, -10, 10, 8],\n [-6, 7, 8, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
188
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[5, 0, -1, 8],\n [-6, 9, -2, 6],\n [-1, 4, 5, 9],\n [4, 5, -3, -10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
51
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[12, 2, 10, 6],\n [-5, 10, 5, -3],\n [11, 11, 10, -8],\n [-5, 4, 7, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
780
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[5, 8, 4, 11],\n [0, -12, -9, -8],\n [0, 0, 1, 3],\n [0, 0, 0, -9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
540
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[3, 9, 6, 0],\n [-3, -3, 10, -2],\n [-11, 3, 0, 10],\n [10, -12, 2, -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"
}
] |
88
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[10, 5, -12, 11],\n [0, -9, -8, 10],\n [0, 0, 12, -1],\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"
}
] |
480
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-8, -8, -5, 6],\n [-7, -2, 1, -7],\n [-12, 5, 4, 10],\n [4, 9, 3, 10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
526
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, -9, 10, -10],\n [-8, -5, 10, 4],\n [8, 10, 10, -10],\n [-6, -9, -5, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
200
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-11, 2, 6, 6],\n [2, 12, -4, -2],\n [6, -4, 0, -2],\n [6, -2, -2, 5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
264
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-2, 0, -2, 2],\n [0, 3, 0, -5],\n [-2, 0, -3, 0],\n [2, -5, 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"
}
] |
968
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, 0, -8, -6],\n [0, -5, 5, 2],\n [-8, 5, 7, -2],\n [-6, 2, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
208
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, 1, 6, -3],\n [0, 9, 4, 11],\n [0, 0, 2, 1],\n [0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
90
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[9, 1, -1, 10],\n [0, 9, 0, 9],\n [0, 0, 3, -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"
}
] |
542
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-11, 5, -6, 4],\n [5, -9, 0, 10],\n [-6, 0, -9, -1],\n [4, 10, -1, -9]]? 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": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, -4, 2, -5],\n [-4, -10, -9, -1],\n [2, -9, -9, 10],\n [-5, -1, 10, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
897
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, 8, -12, -7],\n [8, -9, -6, -6],\n [-12, -6, -8, -1],\n [-7, -6, -1, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
198
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, -4, 4, -4],\n [-4, -12, -2, -4],\n [4, -2, 3, 4],\n [-4, -4, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
840
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[8, -12, -10, -8],\n [-3, -3, 6, 9],\n [8, -5, 1, -6],\n [7, 4, -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"
}
] |
96
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[7, 1, 6, 1],\n [-1, 9, -5, 3],\n [3, -7, -8, 12],\n [10, 4, -12, -7]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
850
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[1, 2, 2, 2],\n [2, -12, 5, -5],\n [2, 5, 11, 4],\n [2, -5, 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"
}
] |
241
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[6, -5, -9, -11],\n [-3, 6, 1, -9],\n [-1, -1, -11, 4],\n [2, -7, -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"
}
] |
133
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-4, 12, 8, -12],\n [0, 7, 11, 1],\n [0, 0, 11, -5],\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"
}
] |
924
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, 3, -1, 4],\n [0, 3, -1, 1],\n [0, 0, 8, -12],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
984
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[9, -11, 1, -7],\n [-9, -2, 12, -3],\n [-8, -12, -12, 10],\n [-6, 4, 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"
}
] |
372
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, -2, -4, 0],\n [-12, 6, -12, -11],\n [8, 5, 8, 6],\n [4, 8, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
485
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[11, 4, -7, -9],\n [0, 2, -6, -1],\n [0, 0, -4, -12],\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"
}
] |
56
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[3, 1, 8, 8],\n [0, 1, 5, 7],\n [0, 0, 12, 6],\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"
}
] |
964
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[11, -9, 6, -1],\n [0, -9, 11, 6],\n [0, 0, -9, 11],\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"
}
] |
455
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[3, -1, -9, -5],\n [-8, -5, 12, -3],\n [4, 1, -10, 3],\n [-6, 2, -4, 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"
}
] |
244
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[4, 12, 8, 8],\n [0, -6, 5, -8],\n [0, 0, 11, -5],\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"
}
] |
152
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[12, -8, 5, -4],\n [-7, -9, -12, 4],\n [-3, 6, 8, -6],\n [2, -7, -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"
}
] |
237
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[2, -6, -4, -1],\n [-5, 7, 12, -6],\n [-1, -10, -2, 7],\n [6, 5, 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"
}
] |
514
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, 2, 0, 0],\n [2, -9, 0, 1],\n [0, 0, 5, 5],\n [0, 1, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-4, 10, -8, 1],\n [2, 12, 8, 5],\n [4, 4, 1, 10],\n [10, 11, -7, 9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
290
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[4, -9, -3, 12],\n [0, 4, -7, 11],\n [0, 0, 9, -6],\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"
}
] |
432
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, 11, -5, 3],\n [7, -11, 4, -3],\n [9, 6, -12, -6],\n [-10, -11, 3, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
216
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 3, -8, 3],\n [12, 10, 3, 8],\n [10, 4, -7, -12],\n [4, -8, -11, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
98
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[10, -7, 8, 1],\n [-7, 8, 0, -4],\n [8, 0, 0, -10],\n [1, -4, -10, 10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-6, 9, -8, 8],\n [9, 1, 2, -3],\n [-8, 2, -2, -6],\n [8, -3, -6, -1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
890
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, -4, -5, 7],\n [-4, 11, 0, -3],\n [-5, 0, 9, 0],\n [7, -3, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
45
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, -5, -6, 3],\n [0, -11, -2, 6],\n [0, 0, -10, 6],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
460
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, -2, -6, 8],\n [0, -5, -2, -1],\n [0, 0, 2, -12],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
900
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, -1, 8, -6],\n [-1, -2, -2, -2],\n [8, -2, 0, 0],\n [-6, -2, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
896
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[1, 1, -11, -1],\n [9, 7, -1, -2],\n [4, -1, -10, 3],\n [7, -2, -8, 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"
}
] |
427
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-7, 0, 3, 5],\n [0, 7, 0, -5],\n [3, 0, -1, -2],\n [5, -5, -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"
}
] |
113
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[1, -10, 1, -7],\n [-10, 6, 3, 5],\n [-4, 5, 1, 7],\n [-5, -12, -11, 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"
}
] |
420
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, -1, 4, 0],\n [-1, -9, 0, -10],\n [4, 0, 9, -2],\n [0, -10, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
633
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-12, -1, -2, 6],\n [-1, 9, 4, 0],\n [-2, 4, -10, 2],\n [6, 0, 2, 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"
}
] |
536
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[0, 7, 1, -4],\n [7, -7, -4, 4],\n [1, -4, -7, 2],\n [-4, 4, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
382
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, -4, 5, -6],\n [-4, 1, -9, 1],\n [5, -9, 8, 7],\n [-6, 1, 7, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
776
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, 4, 2, 5],\n [10, 1, 3, -1],\n [-9, 0, 11, 0],\n [-12, 10, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
912
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-7, -8, -12, -2],\n [0, -4, -12, -5],\n [0, 0, -6, 11],\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, 4, 12, -5],\n [-9, -2, 4, 4],\n [-3, -9, -2, 4],\n [12, 5, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
12
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-2, 2, 5, 0],\n [0, -3, 11, 11],\n [0, 0, 8, -11],\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"
}
] |
424
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, -8, -10, -10],\n [0, 3, 11, 4],\n [0, 0, 1, 4],\n [0, 0, 0, -4]]\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[[-2, -2, -8, -5],\n [-2, 12, -8, 4],\n [-8, -8, -3, -4],\n [-5, 4, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
904
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-2, 5, 11, 1],\n [-6, 7, -12, 8],\n [1, 4, 6, -3],\n [-10, 3, -5, 11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
514
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, 1, 8, 3],\n [1, -2, 10, 2],\n [8, 10, 7, 2],\n [3, 2, 2, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
604
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, 12, 3, -5],\n [-1, -11, -10, 2],\n [-4, 10, -8, -6],\n [3, -9, 9, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
68
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[7, 12, -12, 10],\n [7, 9, 5, 6],\n [12, 9, -4, -6],\n [3, 8, -1, 5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
521
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, -8, 4, 1],\n [-3, -12, 10, -6],\n [12, 6, -7, 5],\n [-11, 8, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
832
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, -7, -7, 12],\n [0, -6, 9, -5],\n [0, 0, -5, 4],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
550
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-5, -9, -7, -4],\n [-9, -10, 8, -2],\n [-7, 8, -9, 6],\n [-4, -2, 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"
}
] |
594
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, -4, -1, 5],\n [0, -5, 3, -7],\n [0, 0, 9, -5],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
480
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[4, 8, 2, 5],\n [6, -6, -1, 0],\n [-2, 5, 8, 10],\n [3, 9, 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"
}
] |
691
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[8, -6, -8, -6],\n [-6, -1, -1, 5],\n [-8, -1, -1, 4],\n [-6, 5, 4, -11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
244
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-10, -12, 12, -6],\n [-11, 9, 11, -1],\n [4, -12, 7, -7],\n [-3, -9, -2, -7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
666
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, -2, 6, -8],\n [9, -2, 3, 2],\n [9, 2, 11, -4],\n [11, 0, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
380
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, 6, 3, 1],\n [0, 5, -7, 2],\n [0, 0, 11, 11],\n [0, 0, 0, 2]]\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, -8, -12, -4],\n [-1, 3, 4, 1],\n [10, 0, 2, -12],\n [1, -7, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
268
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[6, -4, -8, -10],\n [-2, 12, 12, 3],\n [-10, 7, 5, -8],\n [-4, 0, -7, 11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
874
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-11, 12, 5, -3],\n [6, -6, -3, -5],\n [-9, -2, -4, 2],\n [3, 8, 9, 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"
}
] |
76
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, -8, 3, -6],\n [5, -6, -6, 11],\n [-5, -2, -7, -11],\n [-12, -10, -3, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
24
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, 0, 4, -4],\n [-11, -8, 7, 4],\n [-8, 10, 4, -8],\n [11, 12, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
332
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-12, -2, 0, -7],\n [0, -9, -9, 4],\n [0, 0, 8, 11],\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"
}
] |
544
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-5, 0, -6, 8],\n [0, 1, -4, -2],\n [-6, -4, -7, -10],\n [8, -2, -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"
}
] |
899
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, 12, -6, -12],\n [-1, -3, 5, -8],\n [11, 12, -12, -8],\n [-6, 5, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
214
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, -6, 10, 0],\n [-6, 10, 3, -6],\n [10, 3, -7, -7],\n [0, -6, -7, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
519
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, -4, -8, 6],\n [-4, -10, 10, -1],\n [-8, 10, 10, -1],\n [6, -1, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
876
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[4, 0, -5, 12],\n [0, 11, 11, -10],\n [0, 0, -3, 10],\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"
}
] |
812
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, -2, -11, 3],\n [1, 11, 12, 12],\n [11, 2, -8, -9],\n [2, 1, -7, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
902
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[12, -9, 8, 5],\n [-9, 7, 7, 8],\n [8, 7, -10, -2],\n [5, 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"
}
] |
827
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, -7, 0, 7],\n [-7, -6, 2, -4],\n [0, 2, 1, -9],\n [7, -4, -9, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
74
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-9, 11, -7, 7],\n [0, -10, -2, 8],\n [0, 0, -8, -4],\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"
}
] |
400
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, 3, 10, -2],\n [3, -5, 4, -4],\n [10, 4, 11, -6],\n [-2, -4, -6, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
268
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[9, 8, 5, -2],\n [11, -9, -4, -3],\n [-12, -12, -6, 9],\n [-2, 0, -12, -7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
996
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-6, 10, 11, -7],\n [0, 4, 6, -8],\n [0, 0, -8, -5],\n [0, 0, 0, 2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
384
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[8, 4, 2, 2],\n [5, 2, 5, 3],\n [-2, 1, -11, -2],\n [-3, 12, 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"
}
] |
618
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[4, 6, -3, -2],\n [6, 12, -2, 4],\n [-3, -2, -2, 6],\n [-2, 4, 6, 2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
144
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-10, 2, -10, 10],\n [2, -9, -10, -4],\n [-10, -10, 8, -3],\n [10, -4, -3, 10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
186
|
MATH
|
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