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[[3, 11, -11, -1],\n [0, 9, -1, -12],\n [0, 0, 11, 5],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
109
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-10, -10, 0, 9],\n [4, 10, 5, -5],\n [4, -1, -3, 1],\n [-10, 5, 9, -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"
}
] |
944
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[2, -1, -6, 5],\n [-1, -9, 10, -1],\n [-6, 10, -5, -4],\n [5, -1, -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"
}
] |
932
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[2, -1, -5, 0],\n [0, -4, -12, -5],\n [0, 0, 9, -9],\n [0, 0, 0, -3]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
216
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-9, -2, -4, -2],\n [-2, -3, -5, 4],\n [-4, -5, -5, 0],\n [-2, 4, 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"
}
] |
956
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[7, 12, 0, -9],\n [12, -12, 11, 7],\n [0, 11, -1, 4],\n [-9, 7, 4, -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"
}
] |
243
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-10, -4, 3, 2],\n [-4, 3, 2, -8],\n [3, 2, -11, -4],\n [2, -8, -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"
}
] |
304
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, -5, 11, -2],\n [8, 3, 0, 1],\n [8, -1, 2, 2],\n [2, 12, 11, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
699
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 8, 2, 2],\n [-2, -12, -6, 10],\n [-10, -5, -3, 0],\n [-4, 4, 5, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
488
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-6, -12, 6, -4],\n [-12, 10, -2, 4],\n [6, -2, -11, -6],\n [-4, 4, -6, 12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
128
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-7, 0, -1, -2],\n [0, -12, -4, 5],\n [-1, -4, 3, 2],\n [-2, 5, 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"
}
] |
478
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-7, 4, -12, -7],\n [8, 7, 1, -10],\n [-9, 8, 12, -7],\n [11, -3, -11, -6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
736
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, -7, 7, 11],\n [0, -9, 9, 6],\n [0, 0, 3, -4],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
81
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[8, 10, 1, -2],\n [0, -7, -11, 5],\n [0, 0, 1, 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"
}
] |
672
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, -8, 1, -5],\n [0, 6, 0, -10],\n [0, 0, -3, 7],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
838
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, 3, 0, 8],\n [3, 3, -6, 0],\n [0, -6, -1, 4],\n [8, 0, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
644
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[9, -7, -2, -11],\n [-7, 10, -4, 3],\n [-2, -4, 5, 0],\n [-11, 3, 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"
}
] |
446
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, 12, -4, -4],\n [11, -11, -12, 10],\n [7, -9, -11, 7],\n [5, -7, -10, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
466
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-3, -2, 11, 12],\n [0, -7, 1, -6],\n [0, 0, -12, 7],\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"
}
] |
772
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[2, 6, 10, 3],\n [0, -1, -9, 0],\n [0, 0, 8, -12],\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"
}
] |
936
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, -6, -7, 10],\n [-9, -10, -2, 6],\n [10, -6, -7, 5],\n [6, -7, 12, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
971
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, 3, 3, 8],\n [-8, -5, 8, 4],\n [5, 9, 2, 12],\n [-4, -5, -6, -9]]\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[[5, 7, -6, -10],\n [-7, -6, 2, -11],\n [9, 8, 2, 9],\n [-12, -11, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
316
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[9, -4, -4, -2],\n [-4, -2, 4, -2],\n [-4, 4, 0, -8],\n [-2, -2, -8, -5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
760
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 5, -2, 4],\n [5, -4, 2, 0],\n [-2, 2, -11, 10],\n [4, 0, 10, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
328
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-3, 5, -5, 7],\n [-11, 10, 10, -11],\n [-5, 1, 11, 9],\n [-11, -12, 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"
}
] |
460
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[10, -4, -3, 1],\n [-4, 10, 3, 0],\n [-3, 3, 1, 0],\n [1, 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"
}
] |
783
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-11, 1, 11, 11],\n [0, -4, 1, 11],\n [0, 0, -1, 8],\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"
}
] |
396
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-9, -10, -6, -9],\n [-12, -4, 0, -7],\n [-4, -6, -3, 4],\n [-9, -6, 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"
}
] |
410
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, -3, 6, -4],\n [-9, 4, 4, 3],\n [-6, 5, 9, 7],\n [4, 6, 12, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
513
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[7, -7, -3, -7],\n [-2, -3, -3, 2],\n [-1, 2, 12, -8],\n [-4, -11, -2, -3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
171
|
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 [-4, 7, 4, -6],\n [1, 4, 12, -2],\n [8, -6, -2, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
232
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[12, 10, -9, 10],\n [0, 7, 11, -6],\n [0, 0, 9, 8],\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"
}
] |
196
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[8, -2, 8, -7],\n [-2, 7, 0, -10],\n [8, 0, -6, 0],\n [-7, -10, 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"
}
] |
738
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-2, -7, 0, -5],\n [-7, -5, 2, 2],\n [0, 2, -8, 2],\n [-5, 2, 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"
}
] |
560
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[12, 10, 2, 12],\n [0, -2, -7, -9],\n [0, 0, 3, 5],\n [0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
352
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, -2, -6, -1],\n [-2, 4, 2, -2],\n [-6, 2, 6, 2],\n [-1, -2, 2, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
272
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[4, 8, -10, 5],\n [0, 12, -10, -6],\n [8, 8, -10, -11],\n [-3, -1, -8, -10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
800
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-11, 11, 3, 6],\n [11, 10, 4, -9],\n [3, 4, 6, -6],\n [6, -9, -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"
}
] |
523
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-8, -6, -6, 9],\n [0, 6, 11, 8],\n [0, 0, -1, 1],\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"
}
] |
952
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[8, 9, -3, -4],\n [0, -8, -4, -1],\n [0, 0, 9, 4],\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"
}
] |
608
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, -5, -2, -6],\n [0, -2, -12, 6],\n [0, 0, -7, -3],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
916
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-2, -7, 11, -2],\n [-6, -10, 7, -12],\n [-11, -6, 7, 6],\n [3, 12, 12, -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"
}
] |
758
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, 1, 4, 6],\n [1, 12, 0, 5],\n [4, 0, -5, 6],\n [6, 5, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
308
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-4, 8, -5, 12],\n [0, -8, -7, 8],\n [0, 0, 1, 0],\n [0, 0, 0, -4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
872
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[9, -12, -4, -7],\n [0, 8, 2, -11],\n [0, 0, -11, 4],\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"
}
] |
920
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-2, 0, 1, 6],\n [0, 9, -1, -2],\n [1, -1, 1, -4],\n [6, -2, -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"
}
] |
313
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, -4, -10, -10],\n [3, -12, 8, -10],\n [0, 6, -2, 10],\n [9, -6, 9, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
644
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-2, 7, -10, 7],\n [-7, 6, 4, 6],\n [7, 1, 4, 5],\n [6, -10, -11, -12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
952
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[6, 1, 0, -7],\n [1, 3, 0, 6],\n [0, 0, 11, 0],\n [-7, 6, 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"
}
] |
327
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[12, -8, -4, -6],\n [-8, -3, -4, -8],\n [-4, -4, 3, -6],\n [-6, -8, -6, 11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
560
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, 11, -5, -8],\n [3, -7, -10, -1],\n [7, -10, -3, -1],\n [-6, 0, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
105
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[9, -5, 12, -9],\n [0, 8, -6, 7],\n [0, 0, 11, 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"
}
] |
544
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, 5, 10, 6],\n [0, 6, -2, -1],\n [0, 0, -5, -6],\n [0, 0, 0, -2]]\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[[-2, 4, -2, 2],\n [0, 9, -4, -6],\n [10, 12, -12, -4],\n [-11, 7, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
156
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-7, 7, 10, -9],\n [6, -6, 5, 6],\n [-7, 0, -12, 4],\n [5, -1, 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"
}
] |
391
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 9, 9, -11],\n [-6, 4, -3, -11],\n [-3, -8, -1, 5],\n [1, -9, -1, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
503
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[7, 2, -4, 6],\n [2, -11, 6, 6],\n [-4, 6, 9, -6],\n [6, 6, -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"
}
] |
610
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-11, 5, 6, 8],\n [0, 1, -9, 10],\n [0, 0, 4, -11],\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"
}
] |
648
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[8, 3, 6, 1],\n [-7, 1, -3, -3],\n [-8, -4, 0, 12],\n [-1, 2, -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"
}
] |
848
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[12, 4, 0, 9],\n [0, 6, -10, 11],\n [0, 0, -1, 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"
}
] |
72
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, 1, 12, 1],\n [12, 12, 6, 0],\n [-2, 2, -8, -3],\n [-7, 7, 7, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
830
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[2, 7, 12, 10],\n [0, 11, 4, 4],\n [0, 0, 10, -11],\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"
}
] |
660
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[11, -1, -4, 0],\n [-1, 0, 6, 6],\n [-4, 6, -5, 6],\n [0, 6, 6, 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"
}
] |
713
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-7, -10, 8, -9],\n [0, 7, 12, -8],\n [0, 0, -9, -12],\n [0, 0, 0, 4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
764
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, -4, 1, 8],\n [-4, 10, -2, -12],\n [1, -2, 4, 10],\n [8, -12, 10, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
70
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[0, -3, -6, 1],\n [-3, 7, 8, -7],\n [-6, 8, -5, -8],\n [1, -7, -8, -5]]\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[[-8, 10, 2, -4],\n [5, -2, 4, -2],\n [11, -12, -5, -5],\n [5, 5, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
792
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[6, 6, 0, -4],\n [6, -6, -2, 10],\n [0, -2, -9, -8],\n [-4, 10, -8, 11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
80
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, -8, 5, 3],\n [0, 6, 12, 6],\n [0, 0, -3, -5],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
946
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[8, -12, -7, 11],\n [-12, 5, -9, -2],\n [-12, 3, 2, -12],\n [-8, 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"
}
] |
904
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, -4, -8, 5],\n [-5, 9, 1, -3],\n [12, 9, 10, 1],\n [6, 7, -6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
276
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-7, 11, 4, 12],\n [-8, 6, -7, 7],\n [-2, -10, 10, 6],\n [11, 12, -5, -6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
888
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, -3, 3, 2],\n [-3, 10, 1, -2],\n [3, 1, 2, 6],\n [2, -2, 6, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
19
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[4, -1, -7, 4],\n [11, 5, 7, -5],\n [-6, -11, -9, 5],\n [-5, 11, -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"
}
] |
992
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, 0, 2, 12],\n [-8, -8, 5, -9],\n [10, 6, 2, -10],\n [-3, -3, -7, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
808
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-1, -7, 0, 2],\n [1, 10, 7, 0],\n [10, -2, -12, -7],\n [5, 3, -1, -7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
93
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, 2, 2, -10],\n [11, -1, 7, 6],\n [6, 5, -11, -3],\n [6, 7, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
528
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[5, 10, -9, -4],\n [-11, 7, -6, 10],\n [7, -8, -4, 3],\n [9, 0, -6, -12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
469
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[12, 8, -9, 11],\n [0, 8, 9, -3],\n [0, 0, 2, 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"
}
] |
576
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-7, 0, 1, -12],\n [0, -3, -6, 3],\n [0, 0, 11, 8],\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"
}
] |
769
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, 10, 10, 3],\n [0, -9, -1, 6],\n [0, 0, 7, -10],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
921
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, 8, -2, -5],\n [6, 3, -2, 3],\n [9, -6, -6, 3],\n [4, 12, -12, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
338
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[4, -10, -7, -5],\n [0, 5, 9, 11],\n [0, 0, 12, 8],\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"
}
] |
840
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-2, -2, 8, 0],\n [-2, 11, -6, -8],\n [8, -6, -3, 2],\n [0, -8, 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"
}
] |
816
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-10, -5, -12, -9],\n [0, 8, -9, 1],\n [0, 0, -9, 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"
}
] |
520
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, 3, -2, 12],\n [9, 4, -5, 11],\n [-2, -6, -8, -2],\n [-12, 5, -8, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
312
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, 10, -1, 5],\n [-3, 11, 9, -8],\n [4, 9, -10, -3],\n [-4, 8, 12, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
236
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, 5, 11, 1],\n [-7, 6, 4, -3],\n [1, -5, -10, -4],\n [-4, -5, -3, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
256
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, -2, 2, -4],\n [-2, 0, -5, -6],\n [2, -5, 6, 6],\n [-4, -6, 6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
484
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-9, 3, 11, -1],\n [-9, -11, 1, -8],\n [-12, 2, -6, 8],\n [-2, 0, 11, 3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
622
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-5, -6, 1, 1],\n [0, 3, 5, 0],\n [0, 0, -4, -7],\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"
}
] |
880
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[1, 2, -1, -3],\n [0, 7, 6, 6],\n [0, 0, 3, 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"
}
] |
790
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[5, -9, -9, 12],\n [10, 9, 5, -10],\n [9, 3, 10, 6],\n [-2, -1, 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"
}
] |
667
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, -6, -12, 11],\n [5, -6, 0, 9],\n [8, -12, -6, -4],\n [5, 12, -6, -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, 10, -3],\n [-7, -11, -8, 5],\n [1, -12, 0, -6],\n [6, 8, -7, 6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
30
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[10, 10, -1, -10],\n [11, -12, -7, -2],\n [3, 4, 6, -8],\n [-2, 0, -11, 3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
938
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[2, 9, -11, 6],\n [0, -4, -6, -4],\n [0, 0, 11, -2],\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"
}
] |
704
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, -9, 0, 3],\n [-3, 12, -1, -4],\n [-12, -7, -10, -3],\n [-11, 12, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
672
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[5, 0, 1, 1],\n [0, 6, -6, 1],\n [1, -6, 9, -3],\n [1, 1, -3, 3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
76
|
MATH
|
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