messages
listlengths 1
1
| ground_truth
stringclasses 992
values | dataset
stringclasses 1
value |
|---|---|---|
[
{
"content": "What is the determinant of the matrix:\n[[6, -2, 4, 0],\n [-2, 7, 7, 0],\n [4, 7, -9, -1],\n [0, 0, -1, -7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
982
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, 10, -8, 3],\n [0, -2, 12, 7],\n [0, 0, -4, 2],\n [0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
936
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[2, 2, 5, 2],\n [2, -12, -7, 6],\n [5, -7, -1, -8],\n [2, 6, -8, -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"
}
] |
580
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-11, -2, 4, -1],\n [-2, 3, 3, 0],\n [4, 3, 0, -10],\n [-1, 0, -10, -5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
54
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[1, -6, -2, 10],\n [0, -7, -10, -7],\n [0, 0, 2, 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"
}
] |
126
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-10, 2, -6, -8],\n [2, 9, 2, 4],\n [-6, 2, 2, -2],\n [-8, 4, -2, 9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
944
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, -9, -2, 9],\n [7, -8, 5, -11],\n [12, -7, 7, -10],\n [5, 9, 10, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
512
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-3, 8, -1, 4],\n [8, -9, -9, 4],\n [-1, -9, -1, -8],\n [4, 4, -8, 9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
417
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, 0, 6, 2],\n [-2, 9, -12, 4],\n [10, 5, -3, -7],\n [8, 12, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
184
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[11, 6, -12, 5],\n [3, -6, 1, -8],\n [-3, 2, 9, -3],\n [-5, 4, 2, 10]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
218
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-4, -5, 5, -5],\n [0, -2, 3, 6],\n [0, 0, -1, -8],\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"
}
] |
976
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, -11, -2, 4],\n [0, -10, 9, 5],\n [0, 0, 7, -7],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
50
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[9, -4, -8, -2],\n [-4, 2, 6, -2],\n [-8, 6, 8, 1],\n [-2, -2, 1, -8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
470
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, 12, 6, -3],\n [-2, -6, 9, 11],\n [-12, 6, -10, 12],\n [-7, -4, -4, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
984
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[9, -4, 2, 1],\n [-4, 10, 0, -4],\n [2, 0, -8, 6],\n [1, -4, 6, 3]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
336
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-5, 2, 0, 10],\n [2, -7, 4, 3],\n [0, 4, 2, 8],\n [10, 3, 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"
}
] |
100
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[4, 0, 2, 4],\n [0, -4, 2, 3],\n [2, 2, -10, 6],\n [4, 3, 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"
}
] |
524
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-10, 4, 11, 1],\n [0, -2, -6, 5],\n [0, 0, -7, 7],\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"
}
] |
400
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-7, 10, -2, 1],\n [-4, 8, -7, 4],\n [6, 6, -10, -1],\n [1, 9, -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"
}
] |
531
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-8, -9, -5, -9],\n [0, -6, 9, 2],\n [0, 0, -3, 4],\n [0, 0, 0, 7]]? 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": "What is the determinant of the matrix:\n[[-12, -12, 4, -10],\n [0, 10, 7, -10],\n [0, 0, 3, -11],\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"
}
] |
160
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[11, 9, -11, -5],\n [0, -10, -9, 9],\n [0, 0, 6, 4],\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"
}
] |
600
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-12, 7, -8, -4],\n [7, -8, 8, 2],\n [-8, 8, 12, -1],\n [-4, 2, -1, -6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
513
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[12, 1, -7, 0],\n [0, -11, 12, 4],\n [0, 0, 5, -5],\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"
}
] |
640
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-6, -1, 11, 7],\n [-7, 11, -7, -1],\n [-12, 2, -4, -6],\n [-10, 3, -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"
}
] |
474
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[12, -1, 3, 2],\n [-2, 9, -8, -2],\n [8, -8, 5, 3],\n [-2, -1, 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"
}
] |
988
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-6, -2, -2, 0],\n [-2, 10, 6, 2],\n [-2, 6, -4, 6],\n [0, 2, 6, -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"
}
] |
504
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-2, 5, -3, 11],\n [0, -9, -8, -6],\n [0, 0, -6, -11],\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"
}
] |
296
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, 7, -3, 1],\n [-3, 2, 6, -11],\n [-3, -2, 2, 12],\n [0, 6, 11, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
781
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[2, 6, -10, 0],\n [6, 11, 8, -6],\n [-10, 8, -1, 8],\n [0, -6, 8, -2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
620
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[1, 0, -2, -3],\n [0, 2, 3, 7],\n [-2, 3, -9, -2],\n [-3, 7, -2, 2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
418
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-12, -4, 6, 5],\n [-4, -1, -6, -8],\n [6, -6, 8, -2],\n [5, -8, -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"
}
] |
640
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[10, 2, -8, -6],\n [2, -5, 0, 2],\n [-8, 0, -12, -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"
}
] |
328
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-6, -5, 1, -2],\n [-5, 0, -2, 5],\n [1, -2, -7, 0],\n [-2, 5, 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"
}
] |
441
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[10, 1, -11, -4],\n [0, -8, 1, -10],\n [0, 0, -4, 8],\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"
}
] |
120
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, 3, -12, -9],\n [0, -4, 4, 3],\n [0, 0, 5, 1],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
920
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[6, -4, -1, -1],\n [-4, 6, 6, -5],\n [-3, 5, 9, -12],\n [7, -8, 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"
}
] |
629
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-3, -10, 6, 1],\n [-10, 11, -3, 2],\n [6, -3, -10, -2],\n [1, 2, -2, -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"
}
] |
883
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, -1, 12, -6],\n [0, -10, -8, 5],\n [0, 0, 6, 5],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
680
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-12, 6, -4, 0],\n [6, -12, 3, 4],\n [-4, 3, 4, -2],\n [0, 4, -2, 2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
960
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, -8, -11, -8],\n [11, -10, -1, -8],\n [-12, -5, 12, -5],\n [-5, 5, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
590
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-6, -2, 4, 6],\n [-2, -1, -4, 1],\n [4, -4, -2, 2],\n [6, 1, 2, 0]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
580
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-1, 4, -3, -5],\n [4, -10, 7, 3],\n [-3, 7, -4, 1],\n [-5, 3, 1, -1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
141
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-7, 6, 9, -6],\n [6, 10, 2, 5],\n [9, 2, 4, 6],\n [-6, 5, 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"
}
] |
229
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, -5, 8, 4],\n [0, -6, -9, -7],\n [0, 0, 9, -7],\n [0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
864
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, 6, 0, -1],\n [6, 10, -2, 0],\n [0, -2, -12, -3],\n [-1, 0, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
710
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-1, 6, 1, 1],\n [0, 10, -4, -3],\n [0, 0, 9, -12],\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"
}
] |
990
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-12, -11, 1, -7],\n [-7, -3, -1, 7],\n [-1, 12, -5, 7],\n [-12, -12, 5, -7]]\nRound to the nearest integer, then take the result 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[[-7, -10, 9, -12],\n [-12, -2, -4, -10],\n [4, 9, 5, -4],\n [4, 0, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
836
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, -3, 1, -3],\n [-2, -4, 8, -11],\n [-11, 5, -8, 9],\n [-8, 10, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
276
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, 8, 2, 4],\n [8, -8, 6, 0],\n [2, 6, 7, 4],\n [4, 0, 4, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
928
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[1, -1, 11, 1],\n [0, 12, 11, -11],\n [0, 0, -12, 6],\n [0, 0, 0, -7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
8
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, -2, 7, 8],\n [-2, -1, -2, -8],\n [7, -2, 7, -5],\n [8, -8, -5, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
179
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-11, 3, 11, 5],\n [0, -3, 10, 8],\n [0, 0, 5, 11],\n [0, 0, 0, 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"
}
] |
165
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-12, -1, -12, -11],\n [0, -4, 10, 0],\n [0, 0, 8, 9],\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"
}
] |
544
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[9, 8, 0, -2],\n [8, 2, 2, -4],\n [0, 2, -5, -10],\n [-2, -4, -10, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
894
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, -8, 1, 7],\n [0, 10, 12, -12],\n [0, 0, -12, 7],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
640
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-3, 2, -1, 2],\n [2, 6, -2, -8],\n [-1, -2, -6, 8],\n [2, -8, 8, 2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
132
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[0, -6, -2, -4],\n [-6, 10, 2, -3],\n [-2, 2, -11, 0],\n [-4, -3, 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"
}
] |
328
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, 4, -4, 0],\n [4, 10, -1, -6],\n [-4, -1, -4, 12],\n [0, -6, 12, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
529
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, 10, -8, 8],\n [10, -1, -3, -4],\n [-8, -3, 1, 3],\n [8, -4, 3, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
830
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, 3, -4, 7],\n [0, -12, 2, -9],\n [0, 0, -8, -11],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
152
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-12, 8, -4, 7],\n [8, 1, -4, 4],\n [-4, -4, -1, -12],\n [7, 4, -12, 7]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
669
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, -11, 5, 0],\n [5, 7, 7, 3],\n [-7, -7, 12, 9],\n [2, -11, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
643
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[12, 10, 3, 0],\n [0, -3, 5, 10],\n [0, 0, 5, 4],\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"
}
] |
380
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-7, 4, -6, 4],\n [4, -11, 9, 0],\n [-6, 9, 3, 4],\n [4, 0, 4, -6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
524
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-3, 4, -8, 0],\n [0, -12, 10, 4],\n [0, 0, 9, 11],\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"
}
] |
944
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-2, 7, 10, -6],\n [0, -11, 11, -10],\n [0, 0, -8, -6],\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"
}
] |
648
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, 8, -7, 4],\n [0, -9, -9, 4],\n [0, 0, 11, 7],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
752
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 0, 0, 6],\n [0, 10, -7, 1],\n [0, -7, -10, -2],\n [6, 1, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
589
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[8, 11, -4, -10],\n [12, 1, -10, 1],\n [7, 11, -10, 3],\n [3, 3, 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"
}
] |
272
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[12, -4, 12, 12],\n [0, -10, 9, -2],\n [0, 0, -2, 9],\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"
}
] |
520
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-8, -10, 12, 0],\n [0, -10, 7, 1],\n [0, 0, -1, -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"
}
] |
560
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, -12, -5, 9],\n [-2, 3, -6, -12],\n [-5, 10, 5, 2],\n [6, -7, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
883
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-2, 0, 12, 0],\n [0, 4, -4, -6],\n [12, -4, -8, 3],\n [0, -6, 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"
}
] |
32
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-4, -11, -10, 5],\n [-5, -8, 1, 5],\n [10, 10, 0, -6],\n [-10, -2, -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"
}
] |
862
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-2, -12, 5, -5],\n [0, -5, 2, -11],\n [0, 0, -8, -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"
}
] |
960
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-8, 6, 7, -10],\n [0, 11, -10, -11],\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"
}
] |
472
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, -4, -12, -2],\n [0, -1, 7, -5],\n [0, 0, -6, -8],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
18
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-9, -8, -6, 2],\n [-8, -8, -2, -10],\n [-6, -2, 5, -7],\n [2, -10, -7, 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"
}
] |
932
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, 2, 2, 4],\n [2, -7, -2, -5],\n [2, -2, -7, 0],\n [4, -5, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
630
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, 4, -2, 5],\n [4, -8, 1, -7],\n [-2, 1, 2, 8],\n [5, -7, 8, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
261
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, -11, 1, -3],\n [-1, -2, 4, 9],\n [-3, 6, -7, -12],\n [-10, -6, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
546
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-10, -10, -3, 9],\n [10, 8, 12, -3],\n [10, 2, 12, 6],\n [-11, -11, -6, 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"
}
] |
860
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, -12, 9, 7],\n [0, 5, -2, 12],\n [0, 0, -10, -10],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
600
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[11, 7, -11, -3],\n [8, 8, 3, -7],\n [-11, -1, -12, 7],\n [5, -7, 3, -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"
}
] |
80
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-1, 8, 2, 12],\n [1, -12, 1, 4],\n [8, 6, 3, 2],\n [5, -7, 7, 1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
72
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-3, 0, -1, 8],\n [-11, 12, -10, 6],\n [6, 6, -3, 9],\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"
}
] |
907
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, -8, -10, 2],\n [-8, 11, 4, 0],\n [-10, 4, 7, 1],\n [2, 0, 1, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
956
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[11, -11, -2, -3],\n [0, 11, -11, 9],\n [0, 0, -10, 3],\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"
}
] |
320
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-2, -10, 7, -8],\n [-10, -12, 2, 2],\n [7, 2, -3, -6],\n [-8, 2, -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"
}
] |
636
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, 8, -5, 4],\n [0, 8, 7, -7],\n [0, 0, 2, 5],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
520
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[6, -6, -4, -4],\n [4, 0, 12, 9],\n [-6, -9, 8, 7],\n [1, 11, -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"
}
] |
52
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, -5, -5, 0],\n [0, 5, -4, 2],\n [0, 0, -1, 9],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
975
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, 8, 7, -4],\n [8, 9, -4, -2],\n [7, -4, -1, 1],\n [-4, -2, 1, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
465
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[5, -6, 1, -9],\n [-6, -10, -7, 6],\n [1, -7, 10, 0],\n [-9, 6, 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"
}
] |
139
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, 4, 0, 2],\n [4, -10, 2, 4],\n [0, 2, -10, -4],\n [2, 4, -4, -4]]\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[[4, -2, -6, 6],\n [-2, 0, 2, -3],\n [-6, 2, -12, 7],\n [6, -3, 7, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
64
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[7, -3, -9, -10],\n [-1, -7, -5, -8],\n [-1, 10, 9, -1],\n [-7, 11, 1, 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"
}
] |
932
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-10, -7, 1, -1],\n [0, -7, -5, 8],\n [0, 0, 6, 1],\n [0, 0, 0, 2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
840
|
MATH
|
End of preview. Expand
in Data Studio
No dataset card yet
- Downloads last month
- 18