messages
listlengths 1
1
| ground_truth
stringclasses 992
values | dataset
stringclasses 1
value |
|---|---|---|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[12, 4, -6, 0],\n [-3, -1, -3, -3],\n [-11, -9, -10, -5],\n [3, -5, -2, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
800
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, 12, -6, -7],\n [0, 10, 11, -10],\n [0, 0, -10, -8],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
200
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, -2, -8, -6],\n [-2, -2, 6, 0],\n [-8, 6, -11, 0],\n [-6, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
102
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-6, 7, 1, -10],\n [0, 8, -5, -7],\n [0, 0, 8, -4],\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"
}
] |
456
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[6, 0, -10, 0],\n [0, 9, -12, -4],\n [-10, -12, -8, 0],\n [0, -4, 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"
}
] |
564
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, 3, 1, 12],\n [11, 6, 4, 12],\n [-5, 6, 6, 9],\n [10, -12, 6, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
596
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-12, 7, 2, -6],\n [0, -6, 1, -6],\n [0, 0, 7, -2],\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"
}
] |
544
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, 9, 6, 5],\n [0, -4, 12, 2],\n [0, 0, 11, 8],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
264
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-9, -7, -4, 10],\n [2, 6, -9, 6],\n [-8, -2, -9, 8],\n [-5, 7, 3, 10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
232
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, -6, 7, 9],\n [7, -4, 6, -1],\n [2, 0, 7, -8],\n [-4, 9, 11, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
45
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-12, 8, 7, 3],\n [8, 10, 10, -1],\n [7, 10, -12, 4],\n [3, -1, 4, 0]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
993
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-1, 4, 2, 0],\n [-6, 12, 7, -6],\n [7, -7, 2, 4],\n [8, -7, 4, 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"
}
] |
8
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[4, -2, -10, -10],\n [0, -10, 10, -10],\n [0, 0, 3, 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"
}
] |
240
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, 1, 5, 12],\n [0, 6, -8, -5],\n [0, 0, -1, -7],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
12
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[2, 9, 0, 10],\n [-8, 10, 12, 3],\n [5, 9, -11, -7],\n [10, 1, 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"
}
] |
541
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[2, 2, 4, 4],\n [0, -7, -11, -8],\n [0, 0, 1, 2],\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"
}
] |
56
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, -12, 1, -4],\n [0, 11, 9, -3],\n [0, 0, 8, 12],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
744
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[12, 9, 5, -2],\n [0, -11, -12, -9],\n [0, 0, 5, 5],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
40
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[12, 4, -1, -6],\n [-7, 9, -11, 3],\n [-3, -5, 0, 11],\n [-3, 4, 12, -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"
}
] |
276
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-12, 5, 9, 5],\n [0, 5, -12, -9],\n [0, 0, 4, -7],\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, 6, 3, -2],\n [6, -7, 7, -6],\n [3, 7, -3, 4],\n [-2, -6, 4, 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"
}
] |
970
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[4, 10, -2, 10],\n [10, 11, 6, -4],\n [-2, 6, 8, -6],\n [10, -4, -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"
}
] |
836
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-6, -8, 8, -4],\n [-8, 5, 2, 3],\n [8, 2, 1, -10],\n [-4, 3, -10, -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"
}
] |
180
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-1, 2, -2, -9],\n [-8, -2, -11, 12],\n [-6, -1, 3, 8],\n [-4, -6, -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"
}
] |
417
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, -2, -11, -5],\n [-12, -9, 10, -4],\n [-6, 5, -2, -9],\n [-10, 1, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
522
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, 2, -2, 2],\n [2, -9, -4, -2],\n [-2, -4, -1, -2],\n [2, -2, -2, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
904
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[10, 12, -7, 9],\n [6, -6, -11, -5],\n [6, 1, 9, -11],\n [0, 10, 7, -2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
568
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[2, -8, -4, -9],\n [-11, -12, -9, 7],\n [5, 3, 10, 6],\n [4, 0, 5, -5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
427
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-8, 7, -9, -6],\n [-3, 12, -3, -3],\n [-12, -4, -2, 2],\n [11, 5, -3, 6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
200
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[3, 4, -4, 7],\n [-2, -11, -2, -1],\n [-2, 11, -3, -7],\n [-6, 4, -6, 11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
177
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[2, -4, 0, 2],\n [-4, -1, 4, 8],\n [0, 4, 1, -8],\n [2, 8, -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"
}
] |
628
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[3, -8, -9, 2],\n [5, -3, -10, 6],\n [5, -2, 6, 0],\n [6, 1, -12, -9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
205
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[11, 11, -6, 11],\n [0, -1, 3, -12],\n [0, 0, 3, -12],\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"
}
] |
736
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-5, -10, 0, 10],\n [-10, 8, -4, 4],\n [0, -4, 4, 3],\n [10, 4, 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"
}
] |
700
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[2, -2, -6, -8],\n [-2, -3, -2, 1],\n [-6, -2, -12, 6],\n [-8, 1, 6, -12]]\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": "Determine the value of det(A) where A =\n[[12, 4, -7, 7],\n [0, -1, 7, 1],\n [0, 0, -9, -10],\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"
}
] |
864
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, -10, 5, -5],\n [0, -4, -6, -10],\n [0, 0, 12, 1],\n [0, 0, 0, -10]]\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[[11, 1, 8, -2],\n [1, -5, -6, -8],\n [8, -6, 12, 4],\n [-2, -8, 4, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
724
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, 0, -12, 4],\n [0, -11, 0, -1],\n [-12, 0, -7, 4],\n [4, -1, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
808
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-6, -2, 0, -1],\n [-2, -12, -1, -6],\n [0, -1, -11, -4],\n [-1, -6, -4, 0]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
941
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[7, 10, -12, -3],\n [0, 4, -9, -2],\n [0, 0, 3, 2],\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"
}
] |
580
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, 1, 1, 9],\n [-12, -3, 12, 4],\n [-4, -6, -6, -12],\n [7, -2, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
330
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[4, -11, 2, 0],\n [-11, -6, -5, -2],\n [2, -5, 2, -10],\n [0, -2, -10, -2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
856
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-7, -3, 7, 8],\n [-3, 12, -9, 7],\n [-6, -10, -6, -2],\n [5, -12, 5, -3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
108
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[12, -3, 2, -2],\n [-3, 6, -5, 0],\n [2, -5, 9, -6],\n [-2, 0, -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"
}
] |
180
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, -5, 0, -8],\n [-11, 1, -1, -7],\n [-9, 6, -3, -3],\n [2, 3, 7, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
686
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, -11, 10, -11],\n [-4, -4, -5, -11],\n [1, -7, -1, 0],\n [-10, 1, -5, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
949
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[2, -2, 2, 2],\n [-2, -2, 3, 1],\n [2, 3, 6, 2],\n [2, 1, 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"
}
] |
600
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[10, 12, -8, -8],\n [0, 5, 0, -3],\n [0, 0, -6, 5],\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"
}
] |
500
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-3, -6, 8, -6],\n [-6, 2, 10, 10],\n [8, 10, -1, 0],\n [-6, 10, 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"
}
] |
112
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, -3, 11, 10],\n [1, -4, 2, -8],\n [8, 4, 1, -1],\n [12, -3, 9, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
502
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[3, 7, -4, 8],\n [7, -10, 2, -5],\n [-4, 2, 11, 8],\n [8, -5, 8, -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"
}
] |
898
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 0, -2, 6],\n [0, -4, 10, 0],\n [-2, 10, -3, 2],\n [6, 0, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
352
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[3, -8, 10, 7],\n [0, -12, -7, 8],\n [0, 0, -2, -10],\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"
}
] |
648
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[4, 8, 8, 9],\n [0, -8, 11, -1],\n [0, 0, -6, -2],\n [0, 0, 0, 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"
}
] |
960
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, -12, 12, -5],\n [0, -6, -3, 4],\n [0, 0, -4, -4],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
48
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, -6, 6, -4],\n [5, 0, -5, -11],\n [6, -11, -5, -11],\n [-11, -11, 9, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
927
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, 1, -4, -1],\n [10, -2, -6, -8],\n [2, 2, 9, -10],\n [-3, -5, -2, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
8
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-8, -2, 0, 3],\n [0, -6, -8, 5],\n [0, 0, 8, -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"
}
] |
456
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[11, -2, 0, -9],\n [0, 10, 6, 5],\n [0, 0, -7, -5],\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"
}
] |
700
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, -1, -11, -7],\n [-10, -4, -11, -5],\n [-7, -12, 2, 12],\n [-2, 3, -12, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
444
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[6, 4, -1, -1],\n [4, 6, 2, -8],\n [-1, 2, -4, 12],\n [-1, -8, 12, 3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
410
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, -5, 0, 0],\n [-5, -4, 8, 6],\n [0, 8, 9, -8],\n [0, 6, -8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
756
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[12, 7, 10, 3],\n [-5, 5, 9, 1],\n [-1, 5, 7, 9],\n [-7, -12, 2, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
816
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-5, 12, 0, -3],\n [11, 12, 8, -12],\n [-5, 5, -9, 2],\n [-12, 4, -7, -6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
777
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, 7, -10, -5],\n [0, -1, -3, 6],\n [0, 0, -12, 9],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
232
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-7, -1, 0, -8],\n [2, -1, 2, -5],\n [11, 2, 0, 3],\n [6, 7, -7, -10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
966
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[9, 2, 11, 0],\n [10, 8, 7, 7],\n [2, -7, 1, 7],\n [-12, -11, -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"
}
] |
530
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 5, -2, 1],\n [0, -11, -9, 12],\n [0, 0, 9, -10],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
228
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 8, 4, 4],\n [8, -7, -8, -2],\n [4, -8, 7, 2],\n [4, -2, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
218
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-10, 7, -7, -7],\n [7, 11, 1, 3],\n [-7, 1, -2, -2],\n [-7, 3, -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"
}
] |
953
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-10, -8, -11, 3],\n [0, -4, -10, -2],\n [0, 0, -9, -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"
}
] |
760
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[11, -10, -9, 3],\n [0, 2, 3, -12],\n [0, 0, -10, 0],\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"
}
] |
540
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-9, 8, 2, 1],\n [8, -6, 6, 0],\n [2, 6, 3, -11],\n [1, 0, -11, 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"
}
] |
704
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[12, 4, 1, 7],\n [4, -8, 0, 7],\n [1, 0, 5, -2],\n [7, 7, -2, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
293
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-4, 0, 4, 12],\n [0, -4, -10, -5],\n [0, 0, 8, -11],\n [0, 0, 0, 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"
}
] |
640
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-9, 4, 2, 1],\n [-3, -2, -10, 9],\n [8, 1, -9, 9],\n [6, -7, 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"
}
] |
144
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[10, 4, 9, 9],\n [0, -7, -8, 6],\n [0, 0, -7, 3],\n [0, 0, 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"
}
] |
880
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, -2, 4, -4],\n [-2, 12, -1, 1],\n [4, -1, -9, 1],\n [-4, 1, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
842
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[0, 6, 10, 0],\n [6, -11, 0, -7],\n [10, 0, 7, -2],\n [0, -7, -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"
}
] |
124
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-6, 6, 12, -8],\n [0, -9, 11, -2],\n [0, 0, 5, -8],\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"
}
] |
840
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, 2, -12, -7],\n [0, 2, -9, 7],\n [0, 0, -5, -4],\n [0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
990
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-1, -9, -11, -4],\n [-1, -7, 5, -11],\n [9, -11, 9, 8],\n [10, -7, -1, 10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
894
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[6, 10, -6, -10],\n [5, -5, 8, -1],\n [5, -8, 3, 3],\n [-10, 12, -4, 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"
}
] |
660
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[0, 8, -2, 1],\n [-1, 11, -8, -8],\n [-9, -5, 4, 7],\n [10, 1, -3, -4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
514
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[9, 2, 6, -2],\n [2, 11, 0, 4],\n [6, 0, 8, 2],\n [-2, 4, 2, -10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
76
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[0, 2, 8, 6],\n [-6, -7, -1, 11],\n [10, 7, 6, 9],\n [4, 11, 4, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
140
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, 7, -3, 4],\n [0, -1, 9, 5],\n [0, 0, -7, 12],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
84
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[7, -1, -8, -6],\n [4, -1, -8, 8],\n [1, -1, -2, 8],\n [-10, 11, 11, -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"
}
] |
10
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-7, 4, 11, 3],\n [-3, -8, 1, -11],\n [-4, -1, -2, 10],\n [-2, 4, 5, -11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
748
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-8, 5, -2, -2],\n [0, 1, -10, 3],\n [0, 0, -12, 6],\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"
}
] |
672
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[10, -11, 10, 6],\n [0, -10, 5, -9],\n [0, 0, 6, 4],\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"
}
] |
400
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[2, 5, 4, -5],\n [5, 1, 10, -4],\n [4, 10, 0, 5],\n [-5, -4, 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"
}
] |
191
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-7, -8, -6, -6],\n [0, 5, -3, 10],\n [0, 0, -12, -9],\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": "Compute |A| for the matrix A =\n[[6, 7, -4, 0],\n [12, 9, 2, -5],\n [12, -2, 8, 5],\n [3, -10, -3, -7]]\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": "Determine the value of det(A) where A =\n[[11, 5, -11, -10],\n [-8, 11, -9, 10],\n [0, -4, 4, 12],\n [-12, 4, -2, 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"
}
] |
304
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, 5, 5, -11],\n [1, -6, 10, -11],\n [-4, -9, -1, -6],\n [-2, 7, 3, -1]]\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[[-6, 1, -3, 1],\n [3, 3, 12, 0],\n [11, -11, -6, 4],\n [-8, -9, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
772
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-10, 0, 0, 11],\n [-9, 12, 6, 7],\n [-9, 2, -1, 9],\n [-4, -3, -10, -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"
}
] |
715
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[0, -6, -2, -4],\n [-6, -8, -2, 0],\n [-2, -2, 11, -10],\n [-4, 0, -10, -6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
864
|
MATH
|
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