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[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, -4, 6, -1],\n [-4, 1, 0, -10],\n [6, 0, 1, 4],\n [-1, -10, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
607
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-4, 5, 3, -3],\n [0, -12, 12, -3],\n [0, 0, -12, 4],\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" } ]
272
MATH
[ { "content": "What is the determinant of the matrix:\n[[-5, -2, 2, 0],\n [-2, -10, -4, -9],\n [2, -4, -2, -2],\n [0, -9, -2, -9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
654
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, -6, -11, -8],\n [2, 4, -1, 4],\n [0, 11, 4, 12],\n [0, 2, 9, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
789
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-2, -2, -2, 6],\n [-2, -8, -12, 6],\n [-2, -12, 5, 6],\n [6, 6, 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" } ]
704
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, 4, 5, 6],\n [0, 10, -6, -8],\n [0, 0, 8, 5],\n [0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
360
MATH
[ { "content": "Determine the value of det(A) where A =\n[[11, -9, -1, 8],\n [10, -1, -12, -9],\n [12, 8, 7, -6],\n [7, -11, 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" } ]
929
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, -6, -11, 4],\n [0, 8, 4, -3],\n [0, 0, -4, -5],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
288
MATH
[ { "content": "What is the determinant of the matrix:\n[[-6, 1, 1, -7],\n [9, -7, -8, 8],\n [-4, -4, -11, -10],\n [-7, 6, -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" } ]
147
MATH
[ { "content": "What is the determinant of the matrix:\n[[-6, -6, 0, -4],\n [-6, -11, -5, 5],\n [0, -5, -8, 8],\n [-4, 5, 8, -12]]? Round to the nearest integer, then express your answer 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[[4, 10, -7, -9],\n [-3, -5, 1, -8],\n [-11, 6, -12, 3],\n [5, 12, -3, 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" } ]
341
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, -8, -7, -9],\n [-12, 1, -4, 0],\n [-7, 3, 7, 6],\n [1, 10, 8, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
281
MATH
[ { "content": "Determine the value of det(A) where A =\n[[7, 5, 8, -4],\n [0, 7, -12, 12],\n [0, 0, 5, 0],\n [0, 0, 0, -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" } ]
20
MATH
[ { "content": "Determine the value of det(A) where A =\n[[2, 9, 10, -6],\n [-12, -10, 9, 3],\n [-6, -6, -5, -10],\n [9, 0, 5, 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" } ]
3
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, -4, 12, -5],\n [0, -6, 5, -8],\n [0, 0, 9, -2],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
158
MATH
[ { "content": "Determine the value of det(A) where A =\n[[11, 4, -6, -8],\n [4, 7, -3, -1],\n [-6, -3, -12, 7],\n [-8, -1, 7, 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" } ]
110
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, 2, 11, 2],\n [1, -9, 9, 11],\n [5, -6, 6, -12],\n [-5, 8, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
233
MATH
[ { "content": "What is the determinant of the matrix:\n[[-7, 10, 5, 0],\n [-3, 8, 7, 12],\n [-7, -8, 7, 2],\n [-7, 5, 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" } ]
280
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, -7, 9, -9],\n [-6, -4, 3, 3],\n [11, 10, -8, -2],\n [9, -7, -8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
92
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, 4, -8, 8],\n [0, -1, -2, -11],\n [0, 0, -3, 8],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
27
MATH
[ { "content": "Determine the value of det(A) where A =\n[[7, 3, 0, 2],\n [9, 1, 3, -5],\n [9, -2, -4, -12],\n [1, -1, 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" } ]
246
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, -12, 9, -2],\n [8, 8, -12, 10],\n [-2, 12, 3, 11],\n [6, -8, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
832
MATH
[ { "content": "Determine the value of det(A) where A =\n[[5, -4, 3, 5],\n [0, 10, -10, 10],\n [0, 0, -11, 6],\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" } ]
650
MATH
[ { "content": "What is the determinant of the matrix:\n[[-8, 5, 4, -2],\n [0, 7, 3, 6],\n [0, 0, -3, 11],\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" } ]
176
MATH
[ { "content": "Determine the value of det(A) where A =\n[[4, -6, -8, 0],\n [-6, -4, -2, -7],\n [-8, -2, 8, -2],\n [0, -7, -2, 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" } ]
208
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, -10, -7, 5],\n [0, 5, -5, -7],\n [0, 0, -5, -6],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
150
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, 0, -6, 4],\n [0, 1, 2, -4],\n [-6, 2, 11, -3],\n [4, -4, -3, -8]]\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[[-9, -11, 9, -5],\n [6, -2, 5, -9],\n [-3, -9, 12, 5],\n [-4, 4, -2, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
496
MATH
[ { "content": "What is the determinant of the matrix:\n[[-4, 7, 6, -8],\n [-11, 0, 2, 11],\n [-8, 4, -10, -3],\n [7, 12, 9, 1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
565
MATH
[ { "content": "What is the determinant of the matrix:\n[[-3, -10, 3, 6],\n [0, -8, -10, -1],\n [0, 0, -4, 2],\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" } ]
152
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-3, 2, 6, 1],\n [2, 9, -5, 6],\n [6, -5, -5, 5],\n [1, 6, 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" } ]
517
MATH
[ { "content": "Determine the value of det(A) where A =\n[[6, -2, 2, -6],\n [-2, -4, -3, 2],\n [2, -3, 3, 0],\n [-6, 2, 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" } ]
622
MATH
[ { "content": "Determine the value of det(A) where A =\n[[4, -6, 0, 2],\n [0, -8, 12, 8],\n [0, 0, -11, -1],\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" } ]
56
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, 10, 9, -6],\n [2, -6, -4, -9],\n [7, -4, 0, -2],\n [5, -8, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
362
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, -6, -3, 10],\n [-6, 1, 1, -6],\n [-3, 1, 11, -1],\n [10, -6, -1, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
361
MATH
[ { "content": "What is the determinant of the matrix:\n[[-4, -5, -5, 6],\n [-8, 5, 4, -5],\n [-3, -11, -12, -6],\n [-5, 4, 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" } ]
523
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-3, -6, 1, 0],\n [-6, -1, -5, 1],\n [1, -5, 3, -3],\n [0, 1, -3, -9]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
848
MATH
[ { "content": "Determine the value of det(A) where A =\n[[10, 10, -7, -5],\n [0, 2, -1, -12],\n [0, 0, 2, 12],\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" } ]
720
MATH
[ { "content": "Compute |A| for the matrix A =\n[[3, -9, -12, -8],\n [-2, -11, -11, 9],\n [11, -5, -3, -9],\n [-8, 1, 3, -2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
575
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, 1, 3, 3],\n [-12, -1, -9, -1],\n [4, -9, 10, -10],\n [-1, -2, 5, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
636
MATH
[ { "content": "Compute |A| for the matrix A =\n[[5, -8, 9, 7],\n [9, -7, -2, 9],\n [7, 12, -8, -8],\n [0, 1, 9, 0]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
418
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-9, -10, 2, 4],\n [0, 11, -12, -3],\n [0, 0, 1, -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" } ]
307
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-4, -3, -4, -12],\n [0, 5, 3, 4],\n [0, 0, 4, -10],\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" } ]
640
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, -4, 3, 11],\n [2, -7, -11, -9],\n [3, -5, 10, -12],\n [4, -1, 12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
90
MATH
[ { "content": "Compute |A| for the matrix A =\n[[2, 8, 6, 9],\n [0, 1, -11, 11],\n [0, 0, 12, 4],\n [0, 0, 0, -1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
976
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, -8, 2, -3],\n [-2, 3, -5, -12],\n [8, 8, -10, 8],\n [10, -2, -7, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
920
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-11, -4, 3, 1],\n [-4, 8, -2, 2],\n [3, -2, -1, 8],\n [1, 2, 8, -9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
928
MATH
[ { "content": "Determine the value of det(A) where A =\n[[10, 4, -9, 4],\n [4, -12, 0, 0],\n [-9, 0, 3, 0],\n [4, 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" } ]
140
MATH
[ { "content": "Determine the value of det(A) where A =\n[[1, -5, -10, -3],\n [0, 12, -2, 10],\n [0, 0, 2, -7],\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" } ]
264
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 2, -4, 7],\n [-12, 2, -12, -8],\n [9, -6, 7, 0],\n [8, 5, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
510
MATH
[ { "content": "What is the determinant of the matrix:\n[[12, -3, 9, 8],\n [11, -7, -11, 5],\n [10, -12, -5, 10],\n [4, 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" } ]
825
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, 11, 1, 6],\n [-11, 12, 7, -1],\n [-8, 8, -2, -10],\n [-1, 4, 12, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
478
MATH
[ { "content": "Compute |A| for the matrix A =\n[[11, 11, 10, 7],\n [0, -5, -11, 7],\n [0, 0, 1, -10],\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" } ]
835
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, -4, -3, 6],\n [0, -6, 12, 8],\n [0, 0, 9, 0],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
840
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, 5, 1, 5],\n [0, -9, 7, 11],\n [0, 0, -4, -5],\n [0, 0, 0, -2]]\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, 9, -8, 4],\n [12, 4, -8, 11],\n [11, 2, -4, 2],\n [-5, 1, 7, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
103
MATH
[ { "content": "What is the determinant of the matrix:\n[[-8, -2, 0, -9],\n [0, -11, -1, 11],\n [-5, 9, 11, -8],\n [-12, 8, -9, 12]]? 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[[11, 7, 5, -10],\n [0, -5, -6, 1],\n [0, 0, -2, -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" } ]
550
MATH
[ { "content": "Compute |A| for the matrix A =\n[[6, -1, 10, 9],\n [-7, -2, -6, 4],\n [3, -4, 4, -3],\n [9, 4, -10, -1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
250
MATH
[ { "content": "What is the determinant of the matrix:\n[[11, -4, -4, -4],\n [-4, -12, 8, 10],\n [-4, 8, 9, 6],\n [-4, 10, 6, 8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
196
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-7, 6, 0, -3],\n [6, -10, 2, -2],\n [0, 2, 7, 0],\n [-3, -2, 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" } ]
962
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, 12, 2, -1],\n [5, 9, 5, 1],\n [-10, 7, -11, 0],\n [-9, 11, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
298
MATH
[ { "content": "What is the determinant of the matrix:\n[[10, -11, -3, -7],\n [0, 12, -4, 2],\n [0, 0, -11, -1],\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" } ]
680
MATH
[ { "content": "Determine the value of det(A) where A =\n[[12, -6, 6, -1],\n [0, -4, 2, 1],\n [0, 0, 6, -4],\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" } ]
984
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, 6, -6, 2],\n [6, 6, 8, -2],\n [-6, 8, 6, 5],\n [2, -2, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
310
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, -4, -6, -8],\n [-4, -8, -4, 10],\n [-6, -4, 12, 1],\n [-8, 10, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
200
MATH
[ { "content": "Compute |A| for the matrix A =\n[[2, 0, 1, -7],\n [0, 0, 8, 0],\n [1, 8, 9, -1],\n [-7, 0, -1, 9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
984
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-8, 11, -11, 11],\n [0, -11, -7, 7],\n [0, 0, 3, -3],\n [0, 0, 0, 1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
264
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-5, 0, 1, -2],\n [0, 3, 0, 4],\n [1, 0, 6, 5],\n [-2, 4, 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" } ]
274
MATH
[ { "content": "What is the determinant of the matrix:\n[[-2, -1, -4, 1],\n [-1, -5, -6, 2],\n [-4, -6, -11, -6],\n [1, 2, -6, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
211
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 12, -6, 1],\n [-1, 0, 10, -11],\n [1, -1, 10, 7],\n [11, -12, 6, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
716
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-1, 7, 9, -4],\n [7, -10, 4, -8],\n [9, 4, -3, -6],\n [-4, -8, -6, -2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
534
MATH
[ { "content": "What is the determinant of the matrix:\n[[-4, -3, 3, -12],\n [5, 2, 5, -6],\n [7, -4, -6, -2],\n [3, 10, 4, 10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
548
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, -5, 6, 10],\n [-1, -12, 8, 6],\n [5, -3, -6, 0],\n [10, -3, 6, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
528
MATH
[ { "content": "Determine the value of det(A) where A =\n[[11, -11, 4, -1],\n [0, -1, -8, -1],\n [0, 0, -7, 1],\n [0, 0, 0, -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" } ]
230
MATH
[ { "content": "What is the determinant of the matrix:\n[[7, 6, 12, -10],\n [0, 3, 1, 1],\n [0, 0, -5, -6],\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" } ]
50
MATH
[ { "content": "Compute |A| for the matrix A =\n[[3, 9, 0, 2],\n [9, 9, 2, 2],\n [0, 2, 8, -9],\n [2, 2, -9, 10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
574
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, -1, 0, 6],\n [-1, 0, 10, -2],\n [0, 10, -2, -7],\n [6, -2, -7, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
385
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, 6, 2, -10],\n [6, -7, -2, 4],\n [2, -2, -1, -3],\n [-10, 4, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
162
MATH
[ { "content": "What is the determinant of the matrix:\n[[-9, -10, -3, 4],\n [0, 3, 10, -1],\n [0, 0, -11, 8],\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" } ]
79
MATH
[ { "content": "Compute |A| for the matrix A =\n[[6, 1, 0, -1],\n [1, -8, -2, -3],\n [0, -2, -12, 0],\n [-1, -3, 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" } ]
252
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, 5, -10, 5],\n [0, 5, -5, 3],\n [0, 0, -9, 1],\n [0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
350
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, -11, -12, -3],\n [2, 8, 1, -4],\n [10, 11, -7, 11],\n [6, 10, 11, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
52
MATH
[ { "content": "What is the determinant of the matrix:\n[[3, -7, -7, 1],\n [0, 2, 0, 4],\n [0, 0, 1, 4],\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" } ]
940
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 8, -6, 0],\n [8, -9, 10, -2],\n [-6, 10, -11, 2],\n [0, -2, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
942
MATH
[ { "content": "What is the determinant of the matrix:\n[[-3, -4, -4, -6],\n [-1, 6, -2, -2],\n [11, -1, 10, 11],\n [-10, 9, -9, -4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
604
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-12, 0, 6, -2],\n [0, 8, 2, 2],\n [6, 2, 4, 2],\n [-2, 2, 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" } ]
368
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, 2, -2, -2],\n [2, 4, -4, -6],\n [-2, -4, -9, 6],\n [-2, -6, 6, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
208
MATH
[ { "content": "Compute |A| for the matrix A =\n[[12, 2, -5, 7],\n [0, 11, 1, 6],\n [0, 0, 11, -3],\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" } ]
68
MATH
[ { "content": "Determine the value of det(A) where A =\n[[9, 3, -3, 0],\n [3, 12, -7, -2],\n [-3, -7, -9, -9],\n [0, -2, -9, 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" } ]
571
MATH
[ { "content": "What is the determinant of the matrix:\n[[4, 3, -3, -12],\n [-5, -8, 12, 7],\n [-11, -9, -4, -7],\n [10, 2, 9, 6]]? 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": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, -2, 2, -2],\n [-2, -10, -8, 7],\n [2, -8, 12, -6],\n [-2, 7, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
516
MATH
[ { "content": "Compute |A| for the matrix A =\n[[3, -10, 2, -3],\n [0, -5, 4, -9],\n [0, 0, -7, -8],\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" } ]
260
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-7, 4, 5, -12],\n [0, 9, -4, -6],\n [0, 0, 6, -5],\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" } ]
646
MATH
[ { "content": "What is the determinant of the matrix:\n[[11, 3, 0, 7],\n [0, 5, -10, 8],\n [-6, 1, 10, 7],\n [-5, 7, 10, -6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
690
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-7, -12, 8, 8],\n [0, -2, -3, 2],\n [0, 0, -11, 8],\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" } ]
306
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 10, 1, 3],\n [0, -11, 4, 11],\n [0, 0, 5, 5],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
620
MATH
[ { "content": "Compute |A| for the matrix A =\n[[4, 0, -8, 2],\n [0, 12, 5, -1],\n [-8, 5, -1, 4],\n [2, -1, 4, 5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
12
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-5, -12, 1, 11],\n [-3, 7, -6, 6],\n [-1, 2, 8, 12],\n [9, -1, 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" } ]
559
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, -2, 2, 1],\n [-2, 12, 4, 5],\n [2, 4, 4, -10],\n [1, 5, -10, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
580
MATH