messages
listlengths 1
1
| ground_truth
stringclasses 992
values | dataset
stringclasses 1
value |
|---|---|---|
[
{
"content": "What is the determinant of the matrix:\n[[6, 0, 4, -12],\n [0, 5, 1, 3],\n [0, 0, -7, -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"
}
] |
680
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-6, -2, -4, 10],\n [0, 2, 0, 0],\n [0, 0, -12, 2],\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"
}
] |
144
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, 9, 2, 11],\n [0, -5, -10, 6],\n [0, 0, -11, -4],\n [0, 0, 0, -8]]\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[[-4, -4, 11, 8],\n [0, -6, 10, 8],\n [0, 0, 5, -1],\n [0, 0, 0, 1]]\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[[2, 10, 9, -2],\n [10, 6, 1, -10],\n [9, 1, 6, 6],\n [-2, -10, 6, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
160
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[9, 11, 7, 4],\n [0, -11, 12, 10],\n [0, 0, -4, 4],\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"
}
] |
208
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[5, -11, -11, 3],\n [1, 1, 6, -11],\n [12, 9, 7, -4],\n [8, 0, -7, -4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
218
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, -3, 8, -4],\n [-3, -5, 1, -4],\n [8, 1, 1, -4],\n [-4, -4, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
238
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[4, 4, 6, 0],\n [4, -1, -3, -3],\n [6, -3, -6, -3],\n [0, -3, -3, -7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
240
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-12, 3, -11, -5],\n [11, 6, -7, -9],\n [4, 3, 6, 0],\n [-6, -6, 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"
}
] |
701
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, -7, 9, -12],\n [0, -4, 4, 8],\n [0, 0, -3, -2],\n [0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
760
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[0, -6, -3, -5],\n [-6, -10, 4, -2],\n [-3, 4, -10, -2],\n [-5, -2, -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"
}
] |
892
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, 8, 1, 2],\n [8, 11, -3, -8],\n [1, -3, 7, -8],\n [2, -8, -8, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
790
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-12, -3, -10, 0],\n [-3, 7, -4, 9],\n [-10, -4, 1, 6],\n [0, 9, 6, 1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
523
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[9, 8, -2, -2],\n [8, 9, 10, -6],\n [-2, 10, 7, 0],\n [-2, -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"
}
] |
478
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[6, 6, -7, -12],\n [2, 1, -7, 5],\n [6, -3, 11, -1],\n [-1, 1, 7, -11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
670
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[12, 0, -4, -9],\n [0, 3, -4, -1],\n [0, 0, 10, 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"
}
] |
320
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[11, -12, 11, 1],\n [-8, -1, 6, -9],\n [-1, -12, 12, 12],\n [11, 2, 5, -2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
845
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-9, 5, 12, -4],\n [6, -5, -7, 7],\n [4, -3, 1, 12],\n [9, -4, 6, 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"
}
] |
29
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-7, 2, 8, 0],\n [2, -3, 0, -4],\n [8, 0, -3, 1],\n [0, -4, 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"
}
] |
81
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[6, 7, -6, -4],\n [7, 2, 8, 4],\n [-6, 8, -9, 5],\n [-4, 4, 5, 8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
117
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-6, -4, 10, 0],\n [-4, 2, -5, 2],\n [10, -5, 6, -7],\n [0, 2, -7, 4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
684
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, -3, 11, 8],\n [0, -11, 7, -1],\n [0, 0, -10, -6],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
960
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[3, 0, -2, 9],\n [0, 10, -10, -8],\n [0, 0, -3, -12],\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"
}
] |
460
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, -10, -12, 9],\n [0, -9, -9, 10],\n [0, 0, 12, -12],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
352
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[9, -8, -7, 3],\n [8, -2, -9, 4],\n [-1, 4, -11, -3],\n [-3, 7, 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"
}
] |
744
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-11, -1, -10, -2],\n [-1, -5, -5, -6],\n [-10, -5, -10, -3],\n [-2, -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"
}
] |
39
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-10, -12, -11, -1],\n [4, -2, -12, -6],\n [-9, 0, -7, -2],\n [-6, 8, 11, 10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
234
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, -1, 1, -4],\n [0, 8, -11, -12],\n [0, 0, -7, 11],\n [0, 0, 0, -8]]\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[[8, 11, -10, -1],\n [0, -3, -6, 9],\n [0, 0, 3, 5],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
288
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-3, -4, 5, 7],\n [8, -1, 10, 0],\n [4, 4, 7, -9],\n [4, 10, 6, 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"
}
] |
164
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, 11, -3, 11],\n [0, 3, 12, -4],\n [0, 0, 10, -6],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
160
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[5, 3, -5, 5],\n [0, 3, 9, 9],\n [0, 0, -6, 6],\n [0, 0, 0, 12]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
920
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-8, -12, -3, 9],\n [0, 1, 12, -9],\n [0, 0, -8, 7],\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"
}
] |
128
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-3, -12, 12, 6],\n [-12, 7, -10, -8],\n [12, -10, -1, 0],\n [6, -8, 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"
}
] |
508
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, 3, -3, -11],\n [0, 2, 3, 12],\n [0, 0, -5, -12],\n [0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
560
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[10, -7, 11, -4],\n [0, -11, -9, 1],\n [0, 0, 7, 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"
}
] |
150
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-8, 1, 7, -2],\n [0, -3, -3, 3],\n [0, 0, -4, -2],\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"
}
] |
768
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, 12, 9, 11],\n [0, 12, -1, -11],\n [0, 0, -6, 4],\n [0, 0, 0, -4]]\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, 8, 1],\n [0, 4, 10, -6],\n [0, 0, -4, -10],\n [0, 0, 0, -3]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
384
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[4, -10, -8, 10],\n [-10, -3, 2, -2],\n [-8, 2, 10, 7],\n [10, -2, 7, 7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
152
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-2, -6, -7, -1],\n [-6, -2, -6, 8],\n [-7, -6, -9, -4],\n [-1, 8, -4, 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"
}
] |
698
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-6, 1, -9, -1],\n [0, 10, 8, -5],\n [0, 0, -10, -10],\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"
}
] |
200
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, -2, -11, 12],\n [0, -2, -5, -2],\n [0, 0, 8, 6],\n [0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
152
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, -5, -8, -4],\n [12, 6, 11, -7],\n [-7, -7, -7, -11],\n [3, -9, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
635
|
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 [-3, -3, -2, -7],\n [5, 6, -12, 11],\n [-5, 0, -1, -12]]\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[[-2, 0, -2, 5],\n [0, 12, -1, 2],\n [0, 0, -9, 3],\n [0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
944
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-6, -1, -12, 2],\n [-6, -9, -6, 10],\n [10, -9, 3, -2],\n [4, -5, -7, 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"
}
] |
576
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 10, 2, 1],\n [10, 2, -8, -1],\n [2, -8, 9, 4],\n [1, -1, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
301
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-9, 4, 3, 8],\n [0, 1, -12, 0],\n [0, 0, -8, -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"
}
] |
280
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, -5, -8, 1],\n [10, 10, 10, 3],\n [-4, -10, 11, -9],\n [1, -6, 3, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
967
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-12, -1, 3, -10],\n [0, -4, 3, -11],\n [0, 0, 5, -12],\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"
}
] |
560
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-9, 0, 10, -9],\n [0, -8, -4, 2],\n [10, -4, 6, 8],\n [-9, 2, 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"
}
] |
288
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, 1, 7, 7],\n [0, -10, 8, 11],\n [0, 0, -8, -10],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
520
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, 4, 8, 10],\n [0, 10, 4, -4],\n [0, 0, -7, -11],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
300
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-12, -3, 4, 0],\n [-3, -4, 8, 1],\n [4, 8, 12, -1],\n [0, 1, -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"
}
] |
477
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[1, -6, -4, 0],\n [-6, -2, 0, 8],\n [-4, 0, 12, 3],\n [0, 8, 3, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
750
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, -7, 10, -5],\n [0, 7, 11, -11],\n [0, 0, 7, 12],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
490
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[12, -2, -12, 6],\n [-8, 12, 8, -8],\n [-5, 6, -2, 0],\n [-2, -11, -7, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
960
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[8, -10, 10, 1],\n [-10, 7, -12, 4],\n [11, -4, -3, 11],\n [-1, 0, 2, -10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
887
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[11, 6, 8, -4],\n [12, -1, -10, -8],\n [3, 2, 1, 0],\n [9, -10, -7, 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"
}
] |
765
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-3, 7, 8, -7],\n [4, -6, 9, 9],\n [-6, -8, 7, -7],\n [-11, -9, 2, -4]]? 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": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, 4, 6, 5],\n [0, 5, 5, 5],\n [0, 0, -1, -7],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
990
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-3, 3, -4, -9],\n [-2, 4, -3, -9],\n [-11, -9, 11, 0],\n [-11, -5, 5, 1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
966
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[11, -11, 11, 11],\n [0, -9, 8, 1],\n [0, 0, 1, 5],\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"
}
] |
703
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, 8, 6, 11],\n [0, -12, -9, -5],\n [0, 0, 6, -3],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
432
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[7, 0, -2, -8],\n [0, -8, -2, 4],\n [-2, -2, -10, 9],\n [-8, 4, 9, -8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
288
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[11, -9, 4, 3],\n [2, 3, 8, -5],\n [-3, 10, 4, -10],\n [-11, -8, -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"
}
] |
224
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, -11, -3, 9],\n [-3, 11, 5, 7],\n [2, -11, -2, -8],\n [9, -2, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
225
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, 0, -2, -5],\n [0, -1, -1, -5],\n [-2, -1, -12, 8],\n [-5, -5, 8, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
479
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[12, -2, 3, 0],\n [-2, -5, 3, -9],\n [3, 3, -3, -2],\n [0, -9, -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"
}
] |
948
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-6, -5, 9, 8],\n [-5, -4, -6, 0],\n [9, -6, -8, -2],\n [8, 0, -2, 12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
428
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[11, 8, -6, -6],\n [8, 4, -2, -1],\n [-6, -2, 5, 6],\n [-6, -1, 6, -1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
821
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, -2, -3, 1],\n [0, -5, 9, -9],\n [0, 0, 5, -6],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
400
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-9, 10, -7, -6],\n [10, 4, 4, -12],\n [-7, 4, -9, 2],\n [-6, -12, 2, 3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
716
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[8, 2, -2, 1],\n [2, 0, -6, 5],\n [-2, -6, -5, 6],\n [1, 5, 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"
}
] |
24
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, 5, 4, -8],\n [5, 12, 10, 2],\n [4, 10, 12, 8],\n [-8, 2, 8, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
688
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, 12, 8, -6],\n [0, -6, 3, -4],\n [0, 0, -5, -5],\n [0, 0, 0, -9]]\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[[-3, 10, 6, 10],\n [10, -8, -2, -5],\n [6, -2, 10, -7],\n [10, -5, -7, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
414
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-5, 5, -3, -5],\n [0, 12, -9, 12],\n [0, 0, 9, 3],\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"
}
] |
300
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, 0, -7, -2],\n [0, -3, -2, -2],\n [-7, -2, 8, 6],\n [-2, -2, 6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
768
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-11, -3, 3, -12],\n [0, 9, -6, 12],\n [0, 0, 6, 9],\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"
}
] |
436
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[3, 11, -5, -9],\n [-4, 11, 9, 0],\n [3, -10, -3, 10],\n [7, -6, -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"
}
] |
75
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-10, 0, 12, 12],\n [0, -2, -4, -2],\n [0, 0, -11, 3],\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"
}
] |
420
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[7, 3, 3, -5],\n [0, -1, 7, -3],\n [0, 0, -11, 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"
}
] |
539
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, 4, 12, 12],\n [9, 5, 2, -8],\n [2, 5, 1, -7],\n [-11, 6, -11, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
438
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[5, -2, -5, -6],\n [-2, 4, -4, -2],\n [-5, -4, 10, -3],\n [-6, -2, -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"
}
] |
764
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, 11, 12, 12],\n [-5, 0, 7, -1],\n [5, 5, 11, -10],\n [5, -4, -5, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
679
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, -2, -1, 2],\n [-2, 2, 0, 4],\n [-1, 0, -4, 0],\n [2, 4, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
808
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-8, -6, 0, 1],\n [0, 11, 7, 12],\n [0, 0, -1, 5],\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"
}
] |
736
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, -1, 6, 6],\n [0, 5, -6, 12],\n [0, 0, 10, 1],\n [0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, -1, 8, -3],\n [0, -10, 8, -10],\n [0, 0, -5, 0],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
850
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[2, -7, -7, 0],\n [11, 9, 10, 3],\n [0, -8, 6, -1],\n [-7, -2, 5, 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"
}
] |
992
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, 7, 6, -2],\n [7, 11, 6, -9],\n [6, 6, 2, -1],\n [-2, -9, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
527
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, 8, -10, -6],\n [8, -11, -3, -5],\n [-10, -3, 9, 0],\n [-6, -5, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
169
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-3, -4, -4, -6],\n [-4, 5, 7, 1],\n [-4, 7, -1, -8],\n [-6, 1, -8, 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"
}
] |
205
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, 9, -6, -9],\n [4, 2, -7, 5],\n [0, 9, 6, 1],\n [-9, -3, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
859
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, -8, 2, 2],\n [0, -6, -8, -3],\n [0, 0, -4, 11],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
320
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, -1, 1, -10],\n [-1, -9, 10, -6],\n [1, 10, 5, 0],\n [-10, -6, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
538
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-5, 7, 12, 5],\n [0, 4, -1, -6],\n [0, 0, 6, 0],\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"
}
] |
160
|
MATH
|
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