messages
listlengths 1
1
| ground_truth
stringclasses 992
values | dataset
stringclasses 1
value |
|---|---|---|
[
{
"content": "Compute |A| for the matrix A =\n[[-1, -2, 9, 6],\n [0, 12, 5, -7],\n [0, 0, 10, 10],\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"
}
] |
840
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[4, 0, -11, -3],\n [0, 4, -12, -12],\n [0, 0, -11, 8],\n [0, 0, 0, 9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
416
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, 10, -2, -1],\n [0, -4, 6, -10],\n [0, 0, 12, -7],\n [0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
544
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[10, -8, -8, 4],\n [-8, -2, 0, 4],\n [-8, 0, 7, 4],\n [4, 4, 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"
}
] |
384
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[1, -5, 3, -2],\n [0, 4, -5, 9],\n [0, -4, 6, 1],\n [-9, -6, -1, -11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
853
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, 0, 4, -7],\n [0, 4, -10, -8],\n [4, -10, -10, 0],\n [-7, -8, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
772
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, -1, -8, 7],\n [-1, 10, -8, -3],\n [-8, -8, -5, 0],\n [7, -3, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
311
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, 9, -7, 5],\n [0, -9, 9, 1],\n [0, 0, 9, -9],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
595
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, -10, -8, 5],\n [-1, 3, -5, -1],\n [-3, -6, 6, 10],\n [-9, 8, -9, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
805
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, 6, 8, -6],\n [6, 8, -2, 1],\n [8, -2, -4, 0],\n [-6, 1, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
16
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[8, 6, -8, 8],\n [-11, 8, -3, -10],\n [1, -2, -7, 9],\n [-1, 3, 8, -12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
354
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-5, -11, -1, 10],\n [0, 5, -1, -8],\n [0, 0, 12, 8],\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"
}
] |
800
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-11, -9, -6, 4],\n [0, 7, -1, 7],\n [0, 0, -11, -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"
}
] |
71
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, -6, 5, 3],\n [-6, 9, -11, 8],\n [12, -4, -7, 4],\n [3, 12, -1, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
475
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-4, 9, -11, 8],\n [-5, 9, 7, 6],\n [-4, 7, -12, -8],\n [2, 2, 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"
}
] |
757
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[4, -3, 11, 9],\n [0, -5, -1, 4],\n [0, 0, 10, -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"
}
] |
400
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[11, -7, -9, -6],\n [-9, 4, -8, 3],\n [12, 12, 5, 4],\n [-4, -8, 10, 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"
}
] |
904
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, 12, -5, -11],\n [6, -12, 12, 1],\n [4, 11, -9, 11],\n [11, 10, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
470
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[11, 4, 2, 5],\n [4, -2, 0, 2],\n [2, 0, 7, 7],\n [5, 2, 7, -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"
}
] |
40
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[5, -2, -10, 6],\n [-2, -11, -4, 2],\n [-10, -4, 5, 11],\n [6, 2, 11, -11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
284
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-4, 2, -9, 5],\n [0, -6, -9, 10],\n [0, 0, -3, -6],\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"
}
] |
352
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, 4, 8, -12],\n [0, -12, 7, -6],\n [0, 0, 7, -11],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
100
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[12, 2, -6, 7],\n [6, -1, 6, -11],\n [-3, 8, 6, 2],\n [0, 2, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
143
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[10, 7, -8, -1],\n [11, -6, 12, -2],\n [1, 4, 0, 2],\n [0, 0, -6, -11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
208
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-2, -2, -2, -4],\n [-2, -8, -2, 6],\n [-2, -2, -6, 6],\n [-4, 6, 6, -1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
664
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[11, 2, 0, 4],\n [2, -1, 2, -8],\n [0, 2, 1, -1],\n [4, -8, -1, 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"
}
] |
470
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, -11, 10, -9],\n [-11, 4, -8, -3],\n [10, -8, -8, 2],\n [-9, -3, 2, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
496
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, 2, -5, -9],\n [10, 7, -2, -7],\n [-1, 1, 10, -6],\n [-6, 10, 11, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
895
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 6, 10, -5],\n [6, 12, -9, 1],\n [10, -9, 9, 2],\n [-5, 1, 2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
95
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, -9, 12, -8],\n [1, 1, -9, -11],\n [10, -10, 5, -11],\n [-2, 4, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
828
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, -3, -11, -11],\n [-10, 5, 7, 0],\n [-9, 8, 0, 0],\n [-1, -2, 8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
442
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, 4, -4, 6],\n [4, -11, 1, 4],\n [-4, 1, 7, -8],\n [6, 4, -8, 3]]\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[[-11, 0, 0, 4],\n [0, 9, 5, 3],\n [0, 5, -11, -2],\n [4, 3, -2, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
675
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-12, 0, -2, 0],\n [0, -9, -11, -6],\n [-2, -11, -1, 4],\n [0, -6, 4, -8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
608
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[9, -6, 6, 0],\n [-6, -6, -4, 6],\n [6, -4, -9, -3],\n [0, 6, -3, -3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
512
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, 5, -1, 3],\n [12, 8, -3, 5],\n [5, -5, 9, -10],\n [-10, -2, -12, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
696
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[11, -2, -10, -5],\n [0, -10, -6, -10],\n [0, 0, 4, -8],\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"
}
] |
560
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-8, 9, 10, 10],\n [0, -11, 9, -4],\n [0, 0, -2, -12],\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"
}
] |
408
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-1, -1, 10, 0],\n [-1, -7, -8, -10],\n [10, -8, 10, -6],\n [0, -10, -6, -1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
960
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-10, -6, 4, 10],\n [-6, 4, 2, -4],\n [4, 2, -12, 6],\n [10, -4, 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"
}
] |
72
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, 3, 0, -3],\n [3, -9, -8, 0],\n [0, -8, 4, 2],\n [-3, 0, 2, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
764
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[3, 1, -9, 2],\n [12, -3, -11, 10],\n [7, 7, -4, -8],\n [-9, 9, 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"
}
] |
842
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 7, 4, 10],\n [0, -9, 6, 1],\n [0, 0, -11, -3],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
921
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-10, 0, 9, 7],\n [0, -11, 2, -1],\n [0, 0, -8, -6],\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"
}
] |
880
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[12, 2, 0, 10],\n [2, 1, -8, 2],\n [0, -8, 2, -2],\n [10, 2, -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"
}
] |
880
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, 5, 4, 6],\n [7, -8, 7, -11],\n [9, 2, 0, 6],\n [3, -2, -5, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
483
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[2, -7, -7, 11],\n [-7, -8, 6, -1],\n [6, -8, -9, 1],\n [-2, 3, -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"
}
] |
455
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, -3, -1, 0],\n [0, -5, 9, -1],\n [0, 0, 7, -3],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
700
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[9, 12, 1, 5],\n [0, -10, -11, 5],\n [0, 0, 8, 0],\n [0, 0, 0, -3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
160
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[7, -11, 4, 10],\n [-1, 8, -7, -7],\n [-4, 4, -1, -3],\n [4, -8, -10, 5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
561
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, 3, 5, 8],\n [0, -1, -11, 5],\n [0, 0, 10, 0],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
10
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, -3, 9, 9],\n [5, -9, -8, -11],\n [-12, -12, 12, -6],\n [-4, -9, -5, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
300
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-7, 6, -12, -12],\n [-2, -9, 9, -8],\n [5, 10, 1, 7],\n [0, 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"
}
] |
357
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[7, 10, 4, 3],\n [0, -7, -4, 12],\n [0, 0, 7, 0],\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"
}
] |
372
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, -2, -2, 4],\n [-2, 5, -10, 0],\n [-2, -10, 11, -2],\n [4, 0, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
440
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-11, 0, 12, 0],\n [0, -7, -4, -8],\n [0, 0, -4, -5],\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"
}
] |
696
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, 12, -2, -8],\n [0, -3, 12, 12],\n [0, 0, -3, 5],\n [0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
540
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[9, 1, -3, -5],\n [-2, 10, 7, 8],\n [-5, -11, 12, -4],\n [12, 1, -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"
}
] |
399
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[1, 6, -3, -11],\n [-9, 11, 7, 1],\n [7, 1, 1, -2],\n [12, 8, 12, -6]]? Round to the nearest integer, then express your answer modulo 1000.\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[[9, -5, 4, 11],\n [0, 10, 12, -8],\n [0, 0, 4, -4],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
720
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, -11, 0, -6],\n [12, 9, -3, -9],\n [-4, 5, 4, -10],\n [-3, 4, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
452
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, 4, 6, -3],\n [4, 3, -12, 8],\n [6, -12, 4, 6],\n [-3, 8, 6, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
584
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-10, -1, 8, -11],\n [8, -4, 4, 8],\n [-9, 3, 7, 4],\n [3, 12, -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"
}
] |
972
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, 7, -5, 1],\n [0, -1, -7, 7],\n [0, 0, -2, -7],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
984
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-5, 8, 10, 1],\n [0, -6, -1, 8],\n [0, 0, 9, -1],\n [0, 0, 0, -4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
920
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 5, -12, -1],\n [0, -9, 10, 10],\n [12, 9, -10, -9],\n [-6, 12, 3, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
514
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-4, -1, 2, -12],\n [-4, -12, -1, 7],\n [-9, 0, -5, 9],\n [3, -4, 2, 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"
}
] |
795
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[7, 8, 8, 6],\n [8, -12, 0, -2],\n [8, 0, 0, 1],\n [6, -2, 1, -2]]? 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": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, -8, 2, 9],\n [3, 10, -7, 7],\n [4, -2, 1, -9],\n [-9, -10, 12, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
282
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-4, -8, -8, 12],\n [7, 2, -3, -9],\n [10, 7, 2, 11],\n [-2, -5, 11, 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"
}
] |
896
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, -5, 5, 12],\n [12, 4, 4, -3],\n [0, -7, 1, -6],\n [5, 11, -11, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
696
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-11, 8, -2, 9],\n [0, -12, 6, 2],\n [-1, 11, 5, 5],\n [0, -5, 1, 3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
118
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, -5, -1, 4],\n [5, 10, 0, -1],\n [1, -7, 12, -9],\n [9, -9, -4, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-8, -12, 5, -1],\n [-5, 7, -7, -1],\n [5, 3, -3, -12],\n [11, 2, 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"
}
] |
891
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, 10, 6, -11],\n [-5, 4, -11, 4],\n [-8, 11, -2, 1],\n [3, 1, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
337
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[6, -9, -1, -4],\n [0, -4, -10, 9],\n [0, 0, 1, -10],\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"
}
] |
952
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[12, -8, 6, 0],\n [-8, 4, -8, 2],\n [6, -8, 10, -4],\n [0, 2, -4, -3]]\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": "What is the determinant of the matrix:\n[[-11, -10, 8, -1],\n [0, 6, 0, 7],\n [9, 11, 6, -6],\n [-10, -8, -5, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
175
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[4, 1, 8, 0],\n [1, 11, 10, 8],\n [8, 10, -4, 8],\n [0, 8, 8, 12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
72
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, 1, 5, 3],\n [0, 3, 5, 5],\n [0, 0, 10, 11],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
900
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-3, -2, -3, -3],\n [0, -8, 3, 3],\n [0, 0, 7, -7],\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"
}
] |
8
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[6, 6, -2, -7],\n [-7, -12, 0, -5],\n [8, -2, -1, -10],\n [3, 0, -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"
}
] |
742
|
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, 6, -6, -10],\n [-3, -6, -6, 3],\n [7, -10, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
446
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, 4, -8, -8],\n [0, -11, -12, 9],\n [0, 0, -5, -3],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
330
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-1, 1, -2, -7],\n [10, -2, 12, 8],\n [1, -3, 4, -12],\n [9, -12, 4, 5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
692
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, 3, -7, -3],\n [0, -11, -4, -3],\n [0, 0, 6, -8],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
604
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, -9, 3, 5],\n [0, -1, 12, 12],\n [2, 4, 9, -1],\n [-4, 10, 3, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
535
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-7, -6, 1, -8],\n [-6, 1, -10, -2],\n [1, -10, -3, -1],\n [-8, -2, -1, 2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
707
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[2, -5, 4, 12],\n [0, 2, 1, 6],\n [0, 0, 1, -7],\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"
}
] |
980
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[2, -9, -1, -2],\n [-9, -9, -1, -1],\n [-1, -1, -7, 6],\n [-2, -1, 6, 1]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
393
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[5, 3, -5, 1],\n [3, 10, 9, 2],\n [-5, 9, 11, 1],\n [1, 2, 1, 5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
838
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[2, -5, 4, 2],\n [-5, 11, 6, 0],\n [4, 6, -8, 0],\n [2, 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"
}
] |
248
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, 3, 0, 3],\n [3, 11, -1, -2],\n [0, -1, 11, 5],\n [3, -2, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
33
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[2, 0, -1, -3],\n [0, -7, 2, 1],\n [-1, 2, 5, 3],\n [-3, 1, 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"
}
] |
999
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-3, 4, -9, -9],\n [3, -3, -6, 4],\n [11, 0, 8, -5],\n [2, 1, 6, 7]]? 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": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, 6, -10, 11],\n [-12, -3, -4, 1],\n [6, 3, 11, -1],\n [-8, 1, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
644
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, 1, 6, -11],\n [8, 2, 2, 6],\n [2, 0, -10, 9],\n [-10, 12, 8, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
792
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-7, 4, 1, -9],\n [0, -12, -2, 1],\n [0, 0, 4, -10],\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"
}
] |
656
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[5, -11, 2, -4],\n [0, -3, -11, -5],\n [0, 0, 8, -3],\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"
}
] |
720
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, 7, 11, -6],\n [0, -4, 0, -6],\n [0, 0, 1, 4],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
856
|
MATH
|
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