messages
listlengths 1
1
| ground_truth
stringclasses 992
values | dataset
stringclasses 1
value |
|---|---|---|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, -8, 8, -8],\n [0, 4, 4, 11],\n [0, 0, -7, 9],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
320
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[11, -5, -12, 10],\n [2, -4, -5, 6],\n [4, 6, 8, 5],\n [-7, 2, 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"
}
] |
161
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-10, -4, 5, -5],\n [0, -9, 2, -6],\n [0, 0, 1, 3],\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"
}
] |
820
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, 6, 3, -6],\n [0, -9, -3, 12],\n [0, 0, 9, 7],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
327
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, -7, 4, -12],\n [-3, -6, 1, 2],\n [3, -8, -4, 8],\n [1, 12, 12, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
732
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[12, -9, -6, 4],\n [9, -10, 3, 2],\n [-2, 6, -11, 5],\n [-9, -2, -7, -5]]\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[[11, 4, -4, 2],\n [4, -8, -4, 6],\n [-4, -4, -7, 0],\n [2, 6, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
668
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, 6, 11, 4],\n [0, -1, -6, -3],\n [0, 0, -3, -3],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
874
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[1, 9, 6, 4],\n [9, -11, -2, -6],\n [6, -2, 1, -2],\n [4, -6, -2, -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"
}
] |
276
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, -2, -8, 0],\n [-2, 7, 1, -7],\n [-8, 1, 1, 2],\n [0, -7, 2, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
228
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, -6, 0, -2],\n [-6, 10, -6, 1],\n [0, -6, 9, 9],\n [-2, 1, 9, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
15
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-7, 0, 8, -11],\n [0, -1, 0, 9],\n [0, 0, -9, -3],\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"
}
] |
378
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, 1, 7, 10],\n [0, 5, -4, 9],\n [0, 0, -4, -10],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
440
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[12, -5, -4, 2],\n [4, -12, -5, 9],\n [7, 3, -1, -7],\n [-10, 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"
}
] |
268
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, -9, 9, 8],\n [0, 4, 5, -2],\n [0, 0, 7, 4],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
120
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[5, 4, -10, -4],\n [8, 8, 11, 5],\n [3, -6, 6, 1],\n [-11, -5, -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"
}
] |
513
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[2, 7, 1, -9],\n [0, 8, -8, 7],\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"
}
] |
288
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 6, -8, 6],\n [6, 3, 4, -4],\n [-8, 4, 9, 2],\n [6, -4, 2, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
670
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[2, 3, -4, -8],\n [3, 1, 7, 2],\n [-4, 7, 1, 6],\n [-8, 2, 6, -9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
13
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-3, -2, -11, -4],\n [-2, 11, 6, -10],\n [-11, 6, -5, 0],\n [-4, -10, 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"
}
] |
396
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[2, -2, -1, -7],\n [5, 3, 3, 4],\n [0, -8, -5, 1],\n [11, 3, -2, 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"
}
] |
308
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, -6, 4, -6],\n [-6, 3, 5, -2],\n [4, 5, -4, -1],\n [-6, -2, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
320
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[11, -12, -3, 11],\n [0, 12, 8, -5],\n [0, 0, 7, -2],\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"
}
] |
924
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, 6, 7, -4],\n [-12, 8, 1, -10],\n [-3, 10, -12, 2],\n [-3, 9, 9, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
604
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[12, 10, -2, -8],\n [-5, -2, -9, -8],\n [0, -5, -2, -1],\n [-2, -1, 5, -12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
752
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, 7, 1, 1],\n [0, -1, 0, -2],\n [0, 0, 9, 3],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
874
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, -9, 9, -3],\n [5, 10, -7, 12],\n [-5, 1, 9, -1],\n [-2, -3, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
353
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[9, -9, 0, 0],\n [-9, 1, -6, 8],\n [0, -6, 0, -6],\n [0, 8, -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"
}
] |
748
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-1, 2, 6, -7],\n [2, -8, -4, -8],\n [6, -4, -7, -4],\n [-7, -8, -4, -1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
20
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, -7, 8, 3],\n [0, -8, 9, -8],\n [0, 0, -6, -5],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
880
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[2, 5, -5, -1],\n [0, 9, -5, -3],\n [0, 0, -6, 10],\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"
}
] |
80
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[2, 6, -6, 0],\n [6, -8, -6, 4],\n [-6, -6, 11, -8],\n [0, 4, -8, 2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
168
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-2, 2, 4, 1],\n [2, 8, 0, -8],\n [4, 0, 6, 0],\n [1, -8, 0, 0]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
552
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, 11, -1, -6],\n [0, -6, -4, -3],\n [-3, 8, 12, 7],\n [12, -1, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
583
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, 12, 10, -12],\n [0, 1, 5, -8],\n [0, 0, -4, 6],\n [0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
20
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, 5, -11, -8],\n [2, -2, -2, 2],\n [-4, 11, 10, 10],\n [4, 2, -7, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
104
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[12, 12, -2, 3],\n [12, 10, 8, -5],\n [-2, 8, 10, 6],\n [3, -5, 6, -5]]\nRound to the nearest integer, then take the result modulo 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[[0, 4, -3, 4],\n [4, -12, 8, -8],\n [-3, 8, 4, 6],\n [4, -8, 6, -6]]\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[[12, 0, 0, -8],\n [0, 4, 6, 2],\n [0, 6, -1, 11],\n [-8, 2, 11, -4]]\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, 10, -9, 4],\n [8, 4, -12, 8],\n [11, 1, 2, 4],\n [-1, -9, 11, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
888
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, -1, -2, 0],\n [-1, -8, -2, 2],\n [-2, -2, -5, -2],\n [0, 2, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
374
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[11, 10, 4, 1],\n [-11, 6, -5, -3],\n [3, -10, 1, -12],\n [7, 12, 6, 6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
342
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-6, 3, -7, 8],\n [-2, -7, 0, 4],\n [9, 6, -1, -10],\n [-8, 12, 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"
}
] |
865
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-7, -4, 0, -1],\n [0, -3, 1, -3],\n [0, 0, 11, -4],\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"
}
] |
459
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, -5, 0, -2],\n [-9, -8, 0, -3],\n [-5, 9, -3, -3],\n [10, 11, -10, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
909
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, 0, 1, -4],\n [7, 3, 6, -8],\n [-9, -3, -7, -12],\n [0, 1, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
626
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-6, -1, 7, 0],\n [-1, 8, 2, -2],\n [7, 2, -3, 8],\n [0, -2, 8, -11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
159
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 6, 8, 12],\n [6, 7, -1, -2],\n [8, -1, -7, -1],\n [12, -2, -1, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
735
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-12, 6, 4, 4],\n [6, 9, 2, -7],\n [4, 2, -8, 7],\n [4, -7, 7, -12]]? 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": "What is the determinant of the matrix:\n[[5, -9, -8, -5],\n [0, 1, -6, -4],\n [0, 0, -9, 7],\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"
}
] |
405
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[1, -1, -4, 4],\n [-1, -3, -1, 10],\n [-4, -1, 3, 0],\n [4, 10, 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"
}
] |
684
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[0, 0, 0, 4],\n [0, 11, 8, 6],\n [0, 8, -4, 2],\n [4, 6, 2, -4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
728
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 7, 8, -5],\n [-4, -9, -4, -6],\n [-5, -11, -11, 4],\n [-1, -10, 11, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
708
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, -4, 2, 8],\n [-5, 9, 8, -2],\n [-1, -10, 9, 7],\n [11, 6, 10, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
940
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, -3, -3, 2],\n [0, 5, 7, -7],\n [0, 0, 7, -1],\n [0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
680
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, 7, -2, 1],\n [0, 4, 4, -5],\n [0, 0, 8, -9],\n [0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
360
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-9, 12, 11, 7],\n [0, -11, -4, -1],\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"
}
] |
316
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, 4, 11, -6],\n [4, -11, -7, 8],\n [11, -7, 10, 4],\n [-6, 8, 4, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
496
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, -2, -8, 7],\n [-2, 3, -6, 4],\n [-8, -6, -1, -2],\n [7, 4, -2, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
116
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, 7, -8, 2],\n [0, 7, -9, -5],\n [0, 0, -7, 11],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
539
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, -4, -8, -6],\n [-4, -12, 0, -3],\n [-8, 0, -11, -8],\n [-6, -3, -8, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
935
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-4, -10, 6, -5],\n [-10, -5, -7, -4],\n [-6, 9, 10, -4],\n [8, 10, -9, 11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
780
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-9, 3, 1, 5],\n [0, 1, 5, 10],\n [0, 0, -12, -4],\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"
}
] |
812
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, 4, -11, -1],\n [-3, 1, 1, -3],\n [6, 2, -2, -11],\n [-11, 10, -1, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
194
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 3, 4, 2],\n [3, 3, 2, 3],\n [4, 2, 9, 4],\n [2, 3, 4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
470
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-6, -5, 6, -8],\n [0, -11, 2, -11],\n [0, 0, -10, 9],\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"
}
] |
660
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, -11, 10, -11],\n [-11, 7, 9, 12],\n [-6, 4, 3, 1],\n [-11, -2, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
788
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[2, -4, -5, 10],\n [-4, -2, 10, -6],\n [-5, 10, 2, 7],\n [10, -6, 7, -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"
}
] |
626
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[8, -4, -5, 11],\n [-8, -11, -11, 3],\n [-12, 12, 11, -5],\n [9, -2, -10, 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"
}
] |
840
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, -7, 2, -6],\n [-7, -10, -6, -2],\n [2, -6, -1, -10],\n [-6, -2, -10, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
339
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-6, 8, -7, -12],\n [0, -9, 10, -4],\n [0, 0, 7, -8],\n [0, 0, 0, 7]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
646
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[3, 11, 4, 3],\n [-6, 7, 8, -12],\n [-1, 6, 12, -5],\n [-4, 2, 2, -12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
508
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[3, 12, -11, -12],\n [-8, 7, -12, 8],\n [12, 6, -12, -7],\n [0, -4, 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"
}
] |
430
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, -12, 8, -10],\n [11, 7, 1, -7],\n [10, 2, -8, 5],\n [-3, 10, 5, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
843
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-3, -10, -6, -2],\n [-2, 4, 4, 3],\n [1, 7, 4, 7],\n [-7, 10, 2, 1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
416
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-9, -2, 3, -10],\n [11, 2, -10, -5],\n [12, 4, -2, 10],\n [1, -1, -2, 1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
252
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, 11, 5, -11],\n [4, -10, 11, -11],\n [7, -12, 6, 2],\n [-11, 9, 9, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
821
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[5, -9, -3, -10],\n [-9, -8, -9, 4],\n [2, -5, 7, -11],\n [5, 11, -5, 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"
}
] |
849
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, -4, -6, -7],\n [-4, -1, 6, 0],\n [-6, 6, 3, 6],\n [-7, 0, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
393
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[11, -11, 11, -4],\n [0, 1, 2, 1],\n [0, 0, -11, -7],\n [0, 0, 0, 8]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
32
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-7, 12, -8, -10],\n [0, -9, 5, -6],\n [0, 0, 11, 2],\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"
}
] |
307
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[7, 4, 1, 2],\n [4, 1, -3, -5],\n [1, -3, 10, 2],\n [2, -5, 2, -5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
941
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[3, 3, -4, -1],\n [0, 3, 6, -3],\n [0, 0, -4, 3],\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"
}
] |
820
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, -11, -11, -4],\n [-8, -4, -7, 5],\n [6, 0, -10, -6],\n [9, 5, 10, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
264
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, -2, -3, -2],\n [7, 9, -10, -6],\n [1, 9, -1, -6],\n [-5, -7, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[3, -2, 2, -4],\n [-2, 4, -2, 5],\n [2, -2, -1, -6],\n [-4, 5, -6, -3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
147
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[12, -6, 4, -9],\n [0, -12, -2, -11],\n [0, 0, -4, -3],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
696
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[8, -7, -10, -12],\n [0, 3, -11, -10],\n [0, 0, -6, 12],\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"
}
] |
712
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[12, 0, -2, 0],\n [0, -7, 0, 0],\n [-2, 0, -8, -11],\n [0, 0, -11, 9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
464
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, 0, -8, -7],\n [-4, -12, 5, 9],\n [-1, 9, -10, -1],\n [-8, -5, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
899
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-11, 9, -8, 2],\n [0, 1, -12, -3],\n [0, 0, 4, 5],\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"
}
] |
88
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[11, -6, 6, -1],\n [-6, 11, -1, -5],\n [6, -1, 9, 6],\n [-1, -5, 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"
}
] |
427
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[8, -8, 7, -1],\n [7, -1, 9, 6],\n [-4, -6, 2, 10],\n [-6, 11, -10, 2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
976
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, 9, 4, 0],\n [0, -4, 2, 0],\n [0, 0, -5, -1],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
560
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[7, 4, 2, 7],\n [-4, -5, -2, 0],\n [-2, 0, -9, 10],\n [-1, 3, -4, 10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
457
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 9, 2, 8],\n [-9, -9, -3, 9],\n [-3, -5, 0, -2],\n [1, -4, -8, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
334
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 12, -6, -11],\n [7, 9, 7, 2],\n [3, 4, 10, -2],\n [1, -6, -9, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
849
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 2, 11, 0],\n [2, 7, 6, -12],\n [11, 6, -2, -1],\n [0, -12, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
825
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, -12, -6, -5],\n [0, 3, 10, -6],\n [0, 0, -6, 6],\n [0, 0, 0, -11]]\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[[-1, -5, 8, -4],\n [0, 8, -2, -11],\n [0, 0, 9, 11],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
784
|
MATH
|
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