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[ { "content": "Determine the value of det(A) where A =\n[[10, -4, -4, -12],\n [0, -7, -6, -6],\n [0, 0, 10, 0],\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" } ]
200
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, -1, 5, -8],\n [0, 4, 4, 6],\n [0, 0, 4, 6],\n [0, 0, 0, -9]]\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[[-3, 8, 11, 12],\n [7, -5, 4, 1],\n [2, 4, 6, 9],\n [-2, -7, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
519
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, 4, 4, 1],\n [4, -11, -1, 0],\n [4, -1, 1, 1],\n [1, 0, 1, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
257
MATH
[ { "content": "Determine the value of det(A) where A =\n[[7, -2, -3, 10],\n [2, -5, 10, 10],\n [-2, 6, -10, 11],\n [-8, -12, -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" } ]
433
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-3, 9, -3, -12],\n [0, 11, -10, -8],\n [0, 0, -11, 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" } ]
96
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, 10, -5, 10],\n [0, -1, -3, 10],\n [0, 0, -7, 11],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
84
MATH
[ { "content": "What is the determinant of the matrix:\n[[-4, -10, -12, -12],\n [1, -12, -1, 2],\n [-10, 9, -12, 1],\n [9, 4, -7, 2]]? Round to the nearest integer, then express your answer modulo 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, -1, 1, 11],\n [0, -9, 2, 4],\n [0, 0, 2, -7],\n [0, 0, 0, -4]]\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[[-8, 8, 2, 5],\n [0, 9, -11, 10],\n [0, 0, 8, 9],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
456
MATH
[ { "content": "Determine the value of det(A) where A =\n[[1, 9, 1, -9],\n [8, 11, 5, -12],\n [-7, -2, -10, 6],\n [0, 10, 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" } ]
536
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, 11, 4, -10],\n [6, -6, -6, -7],\n [-12, 7, 9, 11],\n [-7, -3, 11, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
327
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, -9, 7, -9],\n [0, 10, 4, 1],\n [0, 0, -6, 0],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
760
MATH
[ { "content": "What is the determinant of the matrix:\n[[-1, 5, -3, -3],\n [0, 7, 11, -12],\n [0, 0, -1, -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" } ]
63
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-4, -2, 9, 0],\n [0, -7, 8, -2],\n [0, 0, -6, -11],\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" } ]
664
MATH
[ { "content": "What is the determinant of the matrix:\n[[-12, 10, 5, -10],\n [0, 3, -5, -10],\n [0, 0, 12, -12],\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" } ]
816
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-3, 4, 7, 1],\n [0, 4, -2, 0],\n [0, 0, 9, 12],\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" } ]
352
MATH
[ { "content": "Determine the value of det(A) where A =\n[[1, 2, -10, 8],\n [-10, -7, 6, 9],\n [7, 0, -11, -3],\n [-8, 11, 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" } ]
558
MATH
[ { "content": "What is the determinant of the matrix:\n[[-8, -12, -7, -3],\n [-10, 1, -2, 5],\n [-9, 10, 3, -11],\n [-8, -9, -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" } ]
27
MATH
[ { "content": "Compute |A| for the matrix A =\n[[9, 7, 3, -9],\n [0, -11, -8, 11],\n [0, 0, -12, 9],\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" } ]
60
MATH
[ { "content": "What is the determinant of the matrix:\n[[-2, 6, -2, -6],\n [6, -7, -3, 5],\n [-2, -3, 10, 7],\n [-6, 5, 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" } ]
140
MATH
[ { "content": "What is the determinant of the matrix:\n[[11, 10, -10, -5],\n [10, 12, 0, 2],\n [-10, 0, 7, -1],\n [-5, 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" } ]
152
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-10, 3, 4, 9],\n [3, -3, -6, -6],\n [4, -6, -12, -10],\n [9, -6, -10, -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" } ]
48
MATH
[ { "content": "Compute |A| for the matrix A =\n[[8, -4, 6, -8],\n [0, -12, 4, -10],\n [0, 0, -10, -2],\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" } ]
440
MATH
[ { "content": "Compute |A| for the matrix A =\n[[2, 8, 0, -4],\n [8, -12, -2, 3],\n [0, -2, -11, -2],\n [-4, 3, -2, -8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
238
MATH
[ { "content": "Compute |A| for the matrix A =\n[[2, 12, -6, -12],\n [-1, -4, 10, -9],\n [7, -12, 6, 8],\n [1, -3, 0, -8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
942
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-5, -9, -7, -10],\n [0, 9, 10, -1],\n [0, 0, -4, -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" } ]
260
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-8, 4, 8, -1],\n [0, 3, -9, 6],\n [0, 0, -1, -11],\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" } ]
144
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-7, 11, 12, -8],\n [0, 5, 4, -7],\n [0, 0, 11, -3],\n [0, 0, 0, -8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
80
MATH
[ { "content": "What is the determinant of the matrix:\n[[4, 1, 4, 6],\n [1, -8, 0, 2],\n [4, 0, -12, -8],\n [6, 2, -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" } ]
776
MATH
[ { "content": "What is the determinant of the matrix:\n[[-7, 7, -1, -1],\n [0, 6, 2, 5],\n [0, 0, 1, 2],\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" } ]
378
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 4, 3, 1],\n [4, 1, 0, -2],\n [3, 0, -8, -10],\n [1, -2, -10, -3]]\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[[-12, -6, -6, 1],\n [0, -12, 11, 1],\n [0, 0, 6, -4],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
496
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, 4, -4, 12],\n [0, -6, 3, -6],\n [0, 0, 7, -5],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
268
MATH
[ { "content": "Compute |A| for the matrix A =\n[[12, -6, 5, -10],\n [-9, -9, 10, 11],\n [-11, -6, 2, -9],\n [10, -12, 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" } ]
442
MATH
[ { "content": "What is the determinant of the matrix:\n[[-7, 0, 0, -2],\n [0, 9, 2, -6],\n [0, 2, 6, 6],\n [-2, -6, 6, 10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
88
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-8, 5, -7, 7],\n [0, 7, -4, -11],\n [0, 0, -8, -5],\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" } ]
552
MATH
[ { "content": "What is the determinant of the matrix:\n[[-6, 4, -9, 3],\n [0, 11, -7, -11],\n [0, 0, 12, -11],\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" } ]
960
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-7, -2, 2, -6],\n [-2, 0, -5, -2],\n [2, -5, -1, 1],\n [-6, -2, 1, 10]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
334
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, -11, 12, -4],\n [-3, 4, -11, 3],\n [6, 7, 3, 4],\n [-10, 11, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
146
MATH
[ { "content": "What is the determinant of the matrix:\n[[-9, 0, -2, -10],\n [10, 2, -4, -3],\n [5, 1, 10, -7],\n [-4, 3, 11, 8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
639
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, -3, 1, -5],\n [-10, 0, 4, -6],\n [9, -8, 5, -11],\n [-5, 12, 12, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
374
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, 1, -4, 0],\n [1, 11, -6, 5],\n [-4, -6, -6, 8],\n [0, 5, 8, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
630
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, -4, 3, -2],\n [-4, -2, -8, 2],\n [3, -8, -2, -4],\n [-2, 2, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
440
MATH
[ { "content": "What is the determinant of the matrix:\n[[10, -3, -4, 11],\n [-3, 0, 6, 4],\n [-4, 6, -4, 8],\n [11, 4, 8, 5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
336
MATH
[ { "content": "What is the determinant of the matrix:\n[[-8, -9, 2, 8],\n [0, -6, 11, -8],\n [0, 0, -1, 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" } ]
760
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, -6, -6, -5],\n [0, 5, 10, 7],\n [0, 0, 6, 12],\n [0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
600
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, -12, 11, 9],\n [5, 12, 4, 4],\n [9, 4, -4, 7],\n [1, 0, -10, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
164
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-12, 5, -1, 9],\n [7, 1, -11, 10],\n [8, 12, 2, -8],\n [-1, -4, -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" } ]
872
MATH
[ { "content": "What is the determinant of the matrix:\n[[-5, -1, -2, -8],\n [12, -4, 6, 10],\n [9, 9, -1, -1],\n [-5, -10, -9, 7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
936
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, -6, 4, 2],\n [-6, 6, 0, 3],\n [4, 0, -7, 6],\n [2, 3, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
111
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, -9, 3, -5],\n [0, -12, 7, 6],\n [0, 0, 2, 3],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
520
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-8, 6, -2, -8],\n [6, 1, 4, 0],\n [-2, 4, -5, 0],\n [-8, 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" } ]
352
MATH
[ { "content": "What is the determinant of the matrix:\n[[4, 1, -5, 2],\n [0, -2, 10, -5],\n [0, 0, -10, -2],\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" } ]
160
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, 4, -6, -7],\n [4, 6, 6, -6],\n [-6, 6, -5, 1],\n [-7, -6, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
814
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, -10, 5, -12],\n [11, 9, 4, 2],\n [9, 1, -9, 11],\n [9, -9, 9, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
116
MATH
[ { "content": "Compute |A| for the matrix A =\n[[7, 12, 3, 10],\n [0, 8, 12, -5],\n [0, 0, 3, -1],\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" } ]
152
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, 0, 12, 6],\n [0, -11, 3, 5],\n [0, 0, 4, 10],\n [0, 0, 0, 6]]\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[[-8, 3, 3, 10],\n [0, -3, -10, -8],\n [0, 0, 4, -1],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
520
MATH
[ { "content": "What is the determinant of the matrix:\n[[-5, 5, 7, 0],\n [5, 9, 6, 9],\n [7, 6, -10, 4],\n [0, 9, 4, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
795
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-7, 10, -4, -8],\n [0, -1, 4, 2],\n [0, 0, -12, 12],\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" } ]
168
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-5, 0, 10, 0],\n [0, -12, 8, 12],\n [0, 0, -11, -11],\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" } ]
320
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-4, -4, 2, -8],\n [-4, 11, 0, 2],\n [2, 0, 8, -8],\n [-8, 2, -8, -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" } ]
80
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, -2, -8, 3],\n [-2, -3, 2, 6],\n [-8, 2, -3, -8],\n [3, 6, -8, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
835
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, -6, 12, -11],\n [0, 11, -5, -6],\n [0, 0, 10, 8],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
160
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, 4, 8, -4],\n [4, 10, -6, -4],\n [8, -6, 8, 11],\n [-4, -4, 11, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
540
MATH
[ { "content": "Determine the value of det(A) where A =\n[[3, 1, -9, 7],\n [5, 10, -2, 10],\n [6, -1, -6, -11],\n [10, 0, -10, -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" } ]
618
MATH
[ { "content": "What is the determinant of the matrix:\n[[-2, 12, -8, -11],\n [0, 6, 11, 10],\n [0, 0, 9, 0],\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" } ]
28
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, 0, -2, 8],\n [1, -11, -6, 12],\n [-7, 1, -5, 0],\n [-11, -4, -12, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
321
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, -4, 4, -10],\n [0, -4, -6, -6],\n [0, 0, -12, -6],\n [0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
696
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, 0, -4, -5],\n [0, -12, 6, -11],\n [-4, 6, -10, 12],\n [-5, -11, 12, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
204
MATH
[ { "content": "What is the determinant of the matrix:\n[[12, 3, 4, -8],\n [3, -7, -2, 0],\n [4, -2, 3, -1],\n [-8, 0, -1, -9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
708
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, 3, 0, -6],\n [3, -11, 2, 7],\n [0, 2, -5, -1],\n [-6, 7, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
58
MATH
[ { "content": "What is the determinant of the matrix:\n[[-11, 7, 8, -2],\n [8, 10, 10, -7],\n [5, -4, -7, -10],\n [-12, -3, -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" } ]
269
MATH
[ { "content": "What is the determinant of the matrix:\n[[9, 8, 2, -8],\n [0, 3, -3, -4],\n [0, 0, -8, -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" } ]
488
MATH
[ { "content": "Compute |A| for the matrix A =\n[[4, 0, -10, 7],\n [11, -3, 8, 10],\n [-1, -9, 9, -7],\n [-8, 2, -5, 5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
40
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, 4, -10, -2],\n [-6, -9, -3, 0],\n [-3, -12, -1, 0],\n [6, -9, -5, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
990
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, -12, 3, 12],\n [0, -4, -12, -9],\n [0, 0, -12, 4],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
920
MATH
[ { "content": "Compute |A| for the matrix A =\n[[8, -5, 2, -5],\n [-7, -6, 10, 11],\n [-12, 3, 12, 8],\n [-7, 0, -7, -8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
479
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-12, 6, 11, -3],\n [7, -10, 2, -7],\n [0, 9, -8, 0],\n [9, -11, 5, 0]]\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": "Compute |A| for the matrix A =\n[[-4, -9, -1, 6],\n [0, -4, -2, 8],\n [0, 0, -6, -11],\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" } ]
56
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, -1, -3, 3],\n [0, -7, 4, -8],\n [0, 0, -6, 5],\n [0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
840
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-2, 12, 4, -1],\n [1, -9, 8, 0],\n [-4, 9, -8, 9],\n [7, 3, 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" } ]
453
MATH
[ { "content": "Compute |A| for the matrix A =\n[[5, 4, 8, 9],\n [0, 9, -9, 4],\n [0, 0, -2, -4],\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" } ]
370
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, -4, 5, 6],\n [-4, -3, 0, 7],\n [-1, 7, 0, 1],\n [-12, 10, -12, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
471
MATH
[ { "content": "What is the determinant of the matrix:\n[[3, 4, 6, 2],\n [4, -1, 3, -4],\n [6, 3, -11, 0],\n [2, -4, 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" } ]
554
MATH
[ { "content": "Determine the value of det(A) where A =\n[[2, 10, 6, 7],\n [-6, 0, 8, 1],\n [4, 0, 11, 11],\n [4, -9, -10, -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" } ]
48
MATH
[ { "content": "What is the determinant of the matrix:\n[[-9, 8, 2, -2],\n [8, -5, -8, -3],\n [2, -8, 5, 0],\n [-2, -3, 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" } ]
264
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-4, -4, 4, 0],\n [-4, 3, 2, 0],\n [4, 2, -2, -7],\n [0, 0, -7, 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" } ]
92
MATH
[ { "content": "What is the determinant of the matrix:\n[[10, 8, -7, 8],\n [0, 8, 9, -12],\n [0, 0, -7, -5],\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" } ]
40
MATH
[ { "content": "Compute |A| for the matrix A =\n[[0, -4, -4, -4],\n [-4, 11, 8, 8],\n [-4, 8, 4, 6],\n [-4, 8, 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" } ]
760
MATH
[ { "content": "Compute |A| for the matrix A =\n[[12, -10, -12, 12],\n [0, 5, 8, 10],\n [0, 0, -9, 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" } ]
940
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, -4, -8, 5],\n [-6, -10, 1, 10],\n [-8, -12, 0, 10],\n [-7, -10, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
540
MATH
[ { "content": "What is the determinant of the matrix:\n[[8, 10, 3, -2],\n [10, 10, -2, -1],\n [3, -2, -6, -5],\n [-2, -1, -5, -9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
235
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-2, 9, 9, -12],\n [0, 11, -1, 5],\n [0, 0, -6, -2],\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" } ]
812
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, -5, -10, 3],\n [0, -3, -8, 10],\n [0, 0, -12, 12],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
320
MATH
[ { "content": "What is the determinant of the matrix:\n[[-6, 2, 4, 4],\n [2, 8, -7, -8],\n [4, -7, 6, -7],\n [4, -8, -7, -4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
596
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, -2, 6, 3],\n [-2, 9, 2, -4],\n [6, 2, -6, 1],\n [3, -4, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
502
MATH
[ { "content": "Compute |A| for the matrix A =\n[[11, -6, 1, 0],\n [-6, 11, -4, -3],\n [1, -4, 11, -10],\n [0, -3, -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" } ]
712
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-8, 6, -12, 6],\n [6, -10, -4, 2],\n [-12, -4, -7, 4],\n [6, 2, 4, 0]]\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