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[[-10, 5, -12, -9],\n [0, -9, -1, 12],\n [0, 0, 3, -1],\n [0, 0, 0, 9]]\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[[-8, -3, 3, 4],\n [4, -1, -2, 5],\n [3, -6, 5, 0],\n [-5, -11, 10, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
40
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[8, 10, -1, -6],\n [-3, 5, -9, -3],\n [-3, 10, 3, 7],\n [9, 1, -11, -10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
559
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[10, -6, -1, -9],\n [0, -6, -11, 10],\n [0, 0, 9, 8],\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"
}
] |
240
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-7, -9, -5, 3],\n [0, -12, 6, -10],\n [0, 0, 4, -7],\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": "Compute |A| for the matrix A =\n[[-12, -12, -2, 12],\n [0, -10, -10, -10],\n [0, 0, 8, -11],\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"
}
] |
400
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, -11, 4, -8],\n [0, 4, 0, 12],\n [0, 0, -1, 4],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
964
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[10, -12, -9, -6],\n [0, 2, -3, 10],\n [0, 0, -1, 7],\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"
}
] |
120
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[3, -7, 12, -6],\n [0, -5, 6, 5],\n [0, 0, 3, -9],\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"
}
] |
865
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, -6, -9, 8],\n [-6, -2, -4, 8],\n [-9, -4, -10, 4],\n [8, 8, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
6
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-3, 2, -7, 8],\n [-11, -1, 5, -12],\n [-7, -3, -5, 10],\n [4, -12, -6, 6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
896
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 6, -8, 0],\n [6, 6, 10, -4],\n [-8, 10, -1, 7],\n [0, -4, 7, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
224
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[11, 10, -12, -12],\n [0, -11, 11, 0],\n [0, 0, 2, -10],\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"
}
] |
758
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-3, 2, -2, 10],\n [1, -10, 7, -11],\n [11, 0, -10, -3],\n [-12, 2, 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"
}
] |
550
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[6, 12, 11, 9],\n [0, -9, 2, -3],\n [0, 0, -11, -3],\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"
}
] |
872
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, -12, 5, -9],\n [-5, 5, -11, -10],\n [0, 6, 8, 6],\n [6, 3, -7, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
76
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-1, -12, -5, 8],\n [-10, 6, -7, 1],\n [9, -2, 3, 5],\n [-3, -8, 10, -4]]\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[[9, 6, 3, -7],\n [6, 0, -10, -2],\n [3, -10, 2, -3],\n [-7, -2, -3, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
932
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[5, -2, 2, 4],\n [-2, 4, 1, 9],\n [2, 1, 0, 0],\n [4, 9, 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"
}
] |
544
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[7, 9, -1, -3],\n [5, -2, 7, 8],\n [-9, 8, 7, -12],\n [-4, 1, 9, 3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
282
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[2, -6, -10, 4],\n [-6, 9, 0, -3],\n [-10, 0, 1, 5],\n [4, -3, 5, 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"
}
] |
516
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, 6, 7, -6],\n [0, 2, 0, 0],\n [0, 0, -4, 11],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
448
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, 1, -9, 4],\n [0, 10, 3, 7],\n [0, 0, -4, -3],\n [0, 0, 0, -12]]\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[[-10, -4, -8, -8],\n [4, -1, 7, 1],\n [-6, 7, -2, -11],\n [-1, 7, -11, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
588
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[12, 8, 2, -3],\n [9, 11, 12, 5],\n [9, -5, 9, 7],\n [0, -6, -2, -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"
}
] |
766
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-11, 6, 5, 2],\n [6, -10, 6, 3],\n [5, 6, 8, -6],\n [2, 3, -6, 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"
}
] |
337
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[0, -2, 6, -9],\n [-3, -7, -10, -12],\n [-7, 5, 3, 12],\n [12, 3, 5, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
963
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-8, -8, 1, -6],\n [-8, 4, 0, -4],\n [1, 0, -3, -2],\n [-6, -4, -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"
}
] |
552
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, -2, 6, -1],\n [-2, 6, -1, 6],\n [6, -1, 7, -2],\n [-1, 6, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
833
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, 6, 1, -11],\n [-9, 12, -9, 10],\n [-6, 8, -1, -6],\n [9, 10, -10, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
246
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-5, -12, -2, -7],\n [-3, -2, -11, 12],\n [4, 11, 10, -8],\n [10, 3, 10, 4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
774
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, 5, -5, -4],\n [0, 5, -9, -7],\n [0, 0, 11, -12],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
780
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, 2, 3, -7],\n [2, -5, 2, 2],\n [3, 2, -10, -8],\n [-7, 2, -8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
618
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, 2, -1, 6],\n [2, -12, 6, 6],\n [-1, 6, 10, 2],\n [6, 6, 2, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
408
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-1, -12, -6, -8],\n [-4, 0, -8, 12],\n [10, -9, 4, -9],\n [1, -8, 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"
}
] |
600
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-12, -6, 2, 3],\n [-6, 5, 2, -4],\n [2, 2, -11, -2],\n [3, -4, -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"
}
] |
491
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-1, -6, 2, -1],\n [0, 6, -5, 10],\n [0, 0, -8, -8],\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"
}
] |
528
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, -9, 1, 9],\n [0, -10, -2, 9],\n [0, 0, -11, -11],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
670
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, 10, 1, -5],\n [-7, -6, 11, 0],\n [0, 7, -1, 7],\n [6, -12, -10, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
104
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-4, 2, 2, 8],\n [2, 8, 2, 4],\n [2, 2, -5, 6],\n [8, 4, 6, 4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
256
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[5, 3, -8, -2],\n [3, 9, 4, -8],\n [-8, 4, 2, -8],\n [-2, -8, -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"
}
] |
304
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-2, 1, 3, -8],\n [11, -9, -11, 8],\n [2, -12, 11, 2],\n [5, 10, -3, -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"
}
] |
494
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-9, 4, 0, 0],\n [4, -1, -6, 1],\n [0, -6, -1, 2],\n [0, 1, 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"
}
] |
890
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[7, -12, 9, 12],\n [0, -5, 9, 9],\n [0, 0, -10, -5],\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"
}
] |
600
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[4, -2, 4, -6],\n [-2, 6, 3, -2],\n [4, 3, 6, -3],\n [-6, -2, -3, 5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
260
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, 0, 9, 10],\n [0, -11, 11, -4],\n [9, 11, 12, 0],\n [10, -4, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
893
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[3, -1, -9, -2],\n [0, -1, -12, 2],\n [0, 0, -3, 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"
}
] |
892
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-10, 12, 1, -4],\n [0, -7, 1, -1],\n [0, 0, -5, 2],\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"
}
] |
900
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[1, -1, 10, -3],\n [0, -12, -3, 5],\n [0, 0, 4, -10],\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"
}
] |
856
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-5, -12, -3, -1],\n [0, -3, 1, -1],\n [0, 0, 5, -9],\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"
}
] |
825
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, 6, 3, 10],\n [0, -1, 6, 1],\n [0, 0, -1, -8],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
993
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-7, 10, 11, -8],\n [0, -9, 6, 12],\n [0, 0, 5, 0],\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"
}
] |
850
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-4, -2, -6, -2],\n [-2, -11, 4, 6],\n [-6, 4, 3, 5],\n [-2, 6, 5, 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"
}
] |
768
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[1, 7, -10, 10],\n [7, -7, -4, 2],\n [-10, -4, 12, -4],\n [10, 2, -4, 6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
544
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-10, 4, -9, 0],\n [-9, 3, -8, 9],\n [7, -2, -10, -3],\n [-8, 6, 10, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
584
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[11, -6, 5, 9],\n [0, 10, -4, 6],\n [0, 0, -6, 1],\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"
}
] |
920
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[0, -12, 5, -11],\n [-5, -4, 5, -10],\n [12, 1, 12, -12],\n [-6, -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"
}
] |
741
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-7, -12, 4, -5],\n [1, 6, 8, 4],\n [-10, -5, -12, -12],\n [10, 7, 9, 12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
43
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, -4, 1, -8],\n [0, -4, -1, 10],\n [0, 0, 4, 12],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
528
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[10, -4, -10, 2],\n [-7, 2, 12, -4],\n [7, 3, 9, -8],\n [9, -5, -11, -6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
788
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[4, 4, 6, 3],\n [4, 12, 6, -7],\n [6, 6, -1, -2],\n [3, -7, -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"
}
] |
408
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[10, 0, -1, 4],\n [0, -4, 2, 2],\n [-1, 2, -6, 4],\n [4, 2, 4, -2]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
636
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-2, 2, 8, 1],\n [0, -7, -10, 1],\n [0, 0, 9, 11],\n [0, 0, 0, 9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
134
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[11, -10, -2, 1],\n [12, -11, -4, -1],\n [0, 3, -12, 5],\n [-11, 2, -7, 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"
}
] |
16
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[7, -11, 7, -8],\n [0, -4, 0, 12],\n [0, 0, 10, 9],\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"
}
] |
880
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 9, -9, 4],\n [-3, 6, -11, -10],\n [0, -3, 7, 8],\n [-10, -7, 2, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
524
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, 10, -2, 7],\n [0, -12, 10, -4],\n [-1, -10, -6, 7],\n [-4, -2, 6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
68
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[4, 2, 6, -7],\n [2, -2, 4, 1],\n [6, 4, -5, 6],\n [-7, 1, 6, -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"
}
] |
674
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-7, 6, -11, -4],\n [-3, 8, -7, -4],\n [-4, -11, -10, 4],\n [-6, -5, -5, 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"
}
] |
408
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, 2, -9, -12],\n [6, -9, 11, -2],\n [5, 4, 6, -3],\n [-5, 0, 12, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
384
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, -2, -10, -1],\n [1, -5, -11, 6],\n [-11, -9, 8, 6],\n [2, -4, 2, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
151
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 10, -12, 1],\n [-6, 4, -5, -10],\n [9, -5, 2, -2],\n [8, -12, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
512
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[8, 9, 0, 7],\n [0, -9, -9, -6],\n [0, 0, 2, -10],\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"
}
] |
432
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-2, -1, -7, 6],\n [-1, -12, -6, 6],\n [-7, -6, 0, 2],\n [6, 6, 2, -6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
480
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, 4, -7, 4],\n [4, -3, 2, -7],\n [-7, 2, 7, -1],\n [4, -7, -1, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
281
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[8, -2, 3, -2],\n [-2, -11, 0, 4],\n [3, 0, 5, -2],\n [-2, 4, -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"
}
] |
336
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, -11, 11, -1],\n [8, 1, -4, 12],\n [6, 6, 4, 0],\n [6, -10, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
492
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-9, 0, -9, -6],\n [0, -4, 2, -4],\n [-9, 2, -4, -8],\n [-6, -4, -8, 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"
}
] |
368
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, -10, 7, -2],\n [2, 12, 2, 0],\n [4, 1, -2, -7],\n [-6, 3, 5, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
892
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, -11, 10, 12],\n [-9, 10, 3, -4],\n [2, -12, 8, 0],\n [5, -2, -10, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
484
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[10, 12, 11, -2],\n [12, 7, 3, 0],\n [11, 3, 1, -2],\n [-2, 0, -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"
}
] |
727
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, -4, 2, 0],\n [-4, 4, -8, 4],\n [2, -8, -11, -3],\n [0, 4, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
696
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[0, 6, -4, -2],\n [0, -1, -9, 8],\n [-3, 7, -11, 1],\n [3, 5, 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"
}
] |
906
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-3, 9, 3, -4],\n [0, 7, 10, 12],\n [0, 0, -11, 9],\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"
}
] |
155
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[3, -3, 6, 0],\n [0, 1, -11, -8],\n [0, 0, -10, 10],\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"
}
] |
790
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-4, -9, -8, 8],\n [-11, 3, -8, -9],\n [8, 6, -2, 6],\n [5, -9, -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"
}
] |
612
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[2, -6, -10, -4],\n [-6, -11, 0, 4],\n [-10, 0, -4, 0],\n [-4, 4, 0, 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"
}
] |
256
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-10, 4, -7, -5],\n [4, 4, -2, -10],\n [-7, -2, 7, -2],\n [-5, -10, -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"
}
] |
188
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-10, -8, 9, 0],\n [-8, 5, 8, 10],\n [9, 8, -1, -8],\n [0, 10, -8, -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"
}
] |
479
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, 5, 3, 2],\n [0, 1, -11, 2],\n [0, 0, -6, 6],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
208
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, 9, -8, 9],\n [9, -3, -2, -6],\n [-8, -2, 8, 2],\n [9, -6, 2, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
488
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-7, 4, 1, -3],\n [11, 8, 8, -4],\n [6, -8, 7, -6],\n [9, 9, -10, 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"
}
] |
443
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-12, 10, 1, -12],\n [11, -12, -1, -6],\n [5, -10, 12, -11],\n [-1, 8, 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"
}
] |
318
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, -8, 5, 9],\n [-2, 11, 8, 5],\n [-8, -4, -5, 10],\n [-1, -9, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[11, -5, 8, -2],\n [-5, 0, -4, -2],\n [8, -4, -12, 0],\n [-2, -2, 0, 9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
580
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, -11, 11, -10],\n [0, -12, -7, 0],\n [0, 0, -8, 10],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
544
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-7, 1, 7, -8],\n [2, 1, 6, -4],\n [1, -8, 6, -8],\n [0, -10, -2, -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"
}
] |
834
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, -7, 3, 4],\n [-7, -5, 1, 5],\n [3, 1, 10, -1],\n [4, 5, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
219
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-6, 0, 10, 2],\n [0, 10, 8, -2],\n [0, 0, -3, -3],\n [0, 0, 0, 10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
800
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[0, 0, -9, 5],\n [8, -9, -4, -12],\n [7, 11, 8, -10],\n [6, 10, -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"
}
] |
14
|
MATH
|
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