messages
listlengths 1
1
| ground_truth
stringclasses 992
values | dataset
stringclasses 1
value |
|---|---|---|
[
{
"content": "Compute |A| for the matrix A =\n[[7, -8, -4, 10],\n [11, -5, -7, 11],\n [1, -10, 11, -10],\n [-11, 3, 9, 1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
746
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, -1, -10, 5],\n [-3, 6, -8, -5],\n [0, -10, 11, -3],\n [10, 6, -7, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
729
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-9, 1, -4, -6],\n [-11, -7, 3, 9],\n [-8, 0, 7, 7],\n [-11, 9, 8, 0]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
444
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-10, 8, 4, 1],\n [-7, -5, 0, 5],\n [6, 3, 9, -10],\n [-11, -11, -6, -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"
}
] |
632
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[10, -8, -4, 4],\n [-8, 7, -1, 0],\n [-4, -1, 12, -3],\n [4, 0, -3, -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"
}
] |
622
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-7, 0, -2, 0],\n [0, -10, -6, 0],\n [-2, -6, -3, 4],\n [0, 0, 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"
}
] |
290
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[11, -2, 4, 2],\n [-2, 2, 0, 6],\n [4, 0, 0, 0],\n [2, 6, 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"
}
] |
832
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, 0, 1, 2],\n [0, -7, 6, 0],\n [1, 6, -5, -4],\n [2, 0, -4, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
272
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[9, -1, 0, 4],\n [-1, -3, 0, 9],\n [0, 0, -12, -2],\n [4, 9, -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"
}
] |
140
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, 2, -10, 8],\n [2, 10, -8, 2],\n [-10, -8, 7, -8],\n [8, 2, -8, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
676
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 8, -11, 5],\n [-10, 8, 4, -8],\n [0, -4, 3, 2],\n [-10, -7, 7, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
310
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, 12, 5, -4],\n [0, -5, 8, 5],\n [0, 0, 3, 6],\n [0, 0, 0, 4]]\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, 8, 1, 0],\n [8, -6, 2, 5],\n [1, 2, 2, -1],\n [0, 5, -1, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
279
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-11, -2, -1, -1],\n [0, -6, 11, -7],\n [0, 0, 10, -8],\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"
}
] |
260
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, 2, 4, -12],\n [-7, 3, 12, 1],\n [9, 10, -2, 0],\n [-2, -12, -10, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
784
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[10, 0, 3, -2],\n [-5, 10, 0, 6],\n [-2, -11, 10, 2],\n [5, 0, 10, -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"
}
] |
165
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-4, -9, -1, -6],\n [0, -3, -8, -8],\n [0, 0, 2, 8],\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"
}
] |
736
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[1, 5, -10, 10],\n [-10, -2, 8, -2],\n [-6, 8, 5, -3],\n [-9, 8, -9, -2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
254
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, 0, 7, 0],\n [0, 9, 5, 0],\n [7, 5, -6, 0],\n [0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
215
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-1, -12, 12, 6],\n [0, 10, 7, -2],\n [0, 0, -9, 1],\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"
}
] |
550
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, -8, -12, -6],\n [-6, -4, 9, -11],\n [-2, 7, -10, 1],\n [3, -3, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
670
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[5, 4, -1, -6],\n [0, -11, 2, 3],\n [0, 0, -2, 1],\n [0, 0, 0, -11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
790
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[9, -10, 4, 11],\n [11, 7, 0, -6],\n [8, -6, 6, 2],\n [2, -8, -3, -2]]? 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[[0, 6, 12, 6],\n [-9, 8, 9, -9],\n [-8, 10, 12, 1],\n [-3, -8, -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"
}
] |
204
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, -4, -8, 10],\n [0, -12, 11, 3],\n [0, 0, -9, 4],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
564
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-4, 3, 12, -12],\n [0, -12, 0, 5],\n [0, 0, 5, 8],\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"
}
] |
880
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-2, 9, -10, 9],\n [9, 8, -4, -8],\n [-10, -4, -6, 8],\n [9, -8, 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"
}
] |
942
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-5, 5, -8, 9],\n [0, 8, 7, -6],\n [0, 0, -9, 6],\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"
}
] |
560
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-7, -12, 3, 8],\n [-12, 1, -7, 3],\n [-9, -4, 12, -3],\n [10, -7, -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"
}
] |
172
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 4, 0, 10],\n [8, -4, 0, 1],\n [7, -12, 8, 4],\n [12, -4, 8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
896
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[3, 8, -1, -6],\n [0, -10, 5, 5],\n [0, 0, -9, 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"
}
] |
80
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-5, -6, -7, -10],\n [6, -8, -5, -7],\n [-3, 0, -10, 0],\n [-3, -8, -5, -9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
944
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-11, 4, 0, 0],\n [4, -3, 1, -10],\n [0, 1, 10, 2],\n [0, -10, 2, -3]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
829
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, -8, -3, -8],\n [-8, 5, -1, -4],\n [-3, -1, -9, 1],\n [-8, -4, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
929
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[6, -1, -6, 8],\n [-1, -12, -2, 2],\n [-6, -2, 8, -1],\n [8, 2, -1, -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"
}
] |
737
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[12, 6, 11, -5],\n [-9, -6, 5, 12],\n [-6, 7, 2, -9],\n [7, 0, 8, -4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
107
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[7, -2, -1, -12],\n [0, 6, 9, 3],\n [0, 0, -1, -11],\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"
}
] |
126
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-9, -2, 6, 7],\n [-2, 2, 2, 6],\n [6, 2, 6, -3],\n [7, 6, -3, 9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
630
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[10, -11, 10, -6],\n [-7, -11, -2, -5],\n [12, -1, 1, -2],\n [-9, 11, 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"
}
] |
680
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, 11, -11, -1],\n [0, -10, 8, 12],\n [0, 0, -7, -3],\n [0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
740
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, -1, -9, 0],\n [0, -1, 9, 2],\n [0, 0, -6, 12],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
928
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, 11, -1, -7],\n [-12, 2, -4, 6],\n [-12, -1, -9, 4],\n [-7, 10, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
418
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[7, -9, -7, -3],\n [-12, 7, -11, -1],\n [-12, 2, 7, -10],\n [3, 0, -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"
}
] |
844
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-1, -6, 2, 9],\n [0, -9, -9, 3],\n [0, 0, 12, 9],\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"
}
] |
756
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[12, 9, -10, 0],\n [0, -8, -11, 6],\n [0, 0, -2, -11],\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"
}
] |
808
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[3, -4, -9, 12],\n [0, 10, 2, -5],\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"
}
] |
350
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, -9, 4, -1],\n [-11, -9, 10, 2],\n [-1, -4, 8, -6],\n [-5, 9, 12, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
594
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[3, -10, 4, -9],\n [-8, -6, 10, -7],\n [-5, -4, -10, 6],\n [-11, 7, -8, -6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
972
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[10, 6, -9, 5],\n [-5, 0, 7, 2],\n [-5, 0, -11, 7],\n [-7, -12, 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"
}
] |
422
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 3, 9, 6],\n [0, 7, 1, 12],\n [0, 0, -2, 1],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
280
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, -4, -6, -2],\n [-4, -11, 0, -5],\n [-6, 0, 11, -1],\n [-2, -5, -1, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
129
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, 0, -2, -5],\n [-6, -11, 4, -5],\n [-5, -4, -1, 1],\n [-2, -5, 4, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
184
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, -7, 5, -10],\n [-2, 7, 12, -4],\n [12, 3, -9, -11],\n [11, 1, 4, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
635
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, -11, 10, 12],\n [8, -9, 11, -3],\n [-8, 9, 5, 3],\n [7, 1, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
856
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, -10, -2, 9],\n [-7, 7, 2, 10],\n [-1, 5, 4, 4],\n [-2, -4, -12, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
460
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[11, 11, -7, -8],\n [0, -12, 6, -1],\n [0, 0, -6, -4],\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": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, 4, -6, -9],\n [-8, 2, 11, 12],\n [1, 5, 9, 12],\n [-7, -3, 2, -6]]\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, 7, -5, -12],\n [-3, -6, -8, -10],\n [-6, -8, 10, -1],\n [11, 3, -9, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
428
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[12, -8, 8, -1],\n [-7, -7, 10, 7],\n [12, 1, -11, -1],\n [-12, -1, 1, 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"
}
] |
298
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[2, 5, -12, 3],\n [-11, 7, 3, 8],\n [11, -11, -10, 2],\n [-10, -10, 1, -1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
701
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-11, -2, 8, 8],\n [-2, 2, -12, 2],\n [8, -12, 0, -4],\n [8, 2, -4, 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"
}
] |
984
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, 4, -8, -10],\n [5, 6, 9, -11],\n [-1, 0, -3, 2],\n [-7, -6, 2, -4]]\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[[-10, 2, 5, 8],\n [0, -7, 2, -1],\n [0, 0, 1, -12],\n [0, 0, 0, 8]]\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, 9, 6, -2],\n [11, -11, 5, 9],\n [-1, 10, -7, 2],\n [-4, -3, -2, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
912
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[4, 3, -8, 8],\n [3, 0, -5, 2],\n [-8, -5, -1, -4],\n [8, 2, -4, -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"
}
] |
977
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[7, -5, 3, 1],\n [-5, -10, -6, -6],\n [3, -6, -9, 6],\n [1, -6, 6, -3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
807
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-10, 5, 0, 9],\n [0, -10, 7, 1],\n [0, 0, -1, 9],\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"
}
] |
900
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[7, 12, 12, -2],\n [0, -6, 12, 9],\n [0, 0, -1, -9],\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"
}
] |
790
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, -4, 6, 2],\n [-4, 7, -3, -1],\n [6, -3, -9, 3],\n [2, -1, 3, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
520
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-10, -10, -11, 8],\n [0, 10, 0, -3],\n [0, 0, -1, -5],\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"
}
] |
900
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[8, 10, -8, 6],\n [0, 12, -4, -8],\n [0, 0, -2, 10],\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"
}
] |
728
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, 12, 7, -7],\n [-1, 6, 9, -3],\n [-11, -7, -9, 3],\n [11, -9, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
658
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-1, -2, -6, 1],\n [-2, 6, -6, 2],\n [-6, -6, 3, -2],\n [1, 2, -2, 2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
578
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, 3, -3, 6],\n [3, -6, -2, 4],\n [-3, -2, -5, 0],\n [6, 4, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
579
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, -6, -3, 3],\n [-12, -1, 5, 10],\n [-2, 8, -9, 11],\n [10, 7, 10, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
383
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[12, -8, -6, -9],\n [0, -8, 2, 12],\n [0, 0, -10, -3],\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"
}
] |
320
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[12, -7, -3, 3],\n [-4, -10, -7, -12],\n [-11, -1, -9, -6],\n [6, -10, 12, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
371
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[5, -9, -4, 0],\n [-9, 12, 1, 4],\n [-4, 1, -1, 4],\n [0, 4, 4, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
264
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[1, -2, 0, 4],\n [-2, 12, -10, 5],\n [0, -10, 5, 2],\n [4, 5, 2, 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"
}
] |
323
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, 9, 5, 7],\n [0, 5, 10, 1],\n [0, 0, -10, 3],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
800
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-9, -3, -8, 8],\n [-2, -11, 3, -6],\n [-8, -5, 11, 3],\n [8, -1, -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"
}
] |
313
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, 6, -8, 0],\n [6, -7, -3, -1],\n [-8, -3, 6, -9],\n [0, -1, -9, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
264
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[12, -1, -2, 11],\n [0, -11, 6, -12],\n [0, 0, 7, 9],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
316
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, 7, -10, -10],\n [0, -9, -1, -5],\n [0, 0, 4, 2],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
40
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[1, 3, 0, -12],\n [6, -6, 9, 9],\n [-4, 3, -4, -6],\n [6, 10, 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"
}
] |
68
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[12, -12, 3, 10],\n [0, -1, -7, 3],\n [0, 0, 3, 1],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
288
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[2, -12, 6, 12],\n [-1, -5, 0, 5],\n [-11, 1, 7, 12],\n [-2, 8, 11, 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"
}
] |
140
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[5, -12, 0, 2],\n [-12, -3, -5, -4],\n [0, -5, -1, -5],\n [2, -4, -5, -8]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
879
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, 7, -11, -11],\n [7, 10, -10, -3],\n [-3, -9, 11, 12],\n [5, -3, -4, 10]]\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[[5, 11, 7, -5],\n [-10, 11, 6, -4],\n [6, -7, 7, 0],\n [-9, 6, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
497
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[0, 10, 6, 2],\n [10, -11, 4, -5],\n [6, 4, -9, -10],\n [2, -5, -10, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
328
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, 5, -1, -7],\n [5, 10, -1, -5],\n [-1, -1, -10, 8],\n [-7, -5, 8, -10]]\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[[12, 0, 7, 9],\n [0, 10, 3, -10],\n [0, 0, 12, 6],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
160
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-12, 10, 8, 2],\n [-9, 5, 0, -9],\n [-7, -3, 4, -5],\n [-12, 5, 8, -3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
720
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-12, 4, 10, 0],\n [4, -8, 2, 4],\n [10, 2, 5, 2],\n [0, 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"
}
] |
848
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, 3, 0, -1],\n [3, -10, 6, 6],\n [0, 6, 6, -7],\n [-1, 6, -7, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
429
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, 12, -6, 10],\n [0, -6, 0, 6],\n [0, 0, -11, -6],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
766
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[12, -9, -1, 1],\n [-9, -12, -11, 6],\n [-1, -11, 8, 2],\n [1, 6, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
283
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-3, 8, 9, 6],\n [8, -5, -10, 0],\n [9, -10, -7, 7],\n [6, 0, 7, -10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
601
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-10, 8, 7, 11],\n [2, 1, -6, 6],\n [-3, -4, 5, -7],\n [0, 3, -7, 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"
}
] |
931
|
MATH
|
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