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[ { "content": "What is the determinant of the matrix:\n[[-6, 7, 10, 4],\n [0, 1, 6, -7],\n [0, 0, -9, 7],\n [0, 0, 0, -5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
730
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, -5, -2, 6],\n [8, -4, -6, -3],\n [-3, -12, 2, 0],\n [4, -7, -5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
863
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-9, -6, 1, 2],\n [0, 9, 0, 11],\n [0, 0, -4, -2],\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" } ]
944
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, 10, -6, 0],\n [3, -12, -7, -8],\n [-11, -11, 2, -5],\n [-3, 8, -11, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
996
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-3, -2, 2, 7],\n [-2, 0, -6, 8],\n [2, -6, -10, -3],\n [7, 8, -3, -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" } ]
580
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 0, -8, -4],\n [0, -11, 5, 10],\n [-8, 5, 3, 2],\n [-4, 10, 2, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
16
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, 0, -8, -6],\n [0, -12, -6, 9],\n [-8, -6, 6, 6],\n [-6, 9, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
732
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, -10, 9, 4],\n [0, 10, 0, 8],\n [0, 0, -4, -9],\n [0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
800
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, -12, -6, -3],\n [0, 4, 12, 9],\n [0, 0, 6, -6],\n [0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
616
MATH
[ { "content": "Compute |A| for the matrix A =\n[[11, 2, 1, -10],\n [2, 3, -4, -7],\n [1, -4, -9, -4],\n [-10, -7, -4, -8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
728
MATH
[ { "content": "Compute |A| for the matrix A =\n[[8, 0, -9, 1],\n [-6, 9, -11, -2],\n [5, -1, -4, -8],\n [0, -3, 9, -12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
256
MATH
[ { "content": "What is the determinant of the matrix:\n[[6, -7, 8, -3],\n [0, 5, -1, -10],\n [0, 0, -1, 1],\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" } ]
850
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, 0, 3, 4],\n [0, 12, -7, -12],\n [0, 0, -9, 9],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
864
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-9, 10, -7, 6],\n [0, 12, -9, 1],\n [0, 0, 12, 10],\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" } ]
184
MATH
[ { "content": "Compute |A| for the matrix A =\n[[4, -11, 3, 8],\n [-11, -6, -2, -6],\n [3, -2, -9, 3],\n [8, -6, 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" } ]
75
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, -5, -9, -3],\n [0, -11, 2, 1],\n [0, 0, -3, 3],\n [0, 0, 0, -8]]\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[[4, -2, -2, -3],\n [-2, -6, 4, -5],\n [-2, 4, -3, 3],\n [-3, -5, 3, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
726
MATH
[ { "content": "What is the determinant of the matrix:\n[[9, -6, 6, 11],\n [10, -7, 5, -12],\n [7, -6, -9, -7],\n [-8, -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" } ]
201
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, -12, 5, -11],\n [2, 9, 0, -4],\n [9, -10, 11, 0],\n [-7, 10, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
327
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, -9, 9, 2],\n [-4, 9, 12, 6],\n [-4, -2, 10, 6],\n [4, 3, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
408
MATH
[ { "content": "Determine the value of det(A) where A =\n[[6, -7, 8, 0],\n [-7, 12, 0, 2],\n [8, 0, -2, -8],\n [0, 2, -8, 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" } ]
272
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, -6, 5, 12],\n [0, -6, -2, 1],\n [0, 0, 10, -11],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
160
MATH
[ { "content": "Compute |A| for the matrix A =\n[[2, -8, -3, 4],\n [-1, 1, -3, -11],\n [-2, 1, 11, -4],\n [12, -1, 4, -10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
314
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, 6, -3, -2],\n [0, -10, -3, -1],\n [0, 0, -1, -6],\n [0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
80
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-2, 6, -4, -1],\n [-11, -11, 4, -8],\n [-5, -7, -9, -6],\n [-11, 4, -12, 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" } ]
647
MATH
[ { "content": "Determine the value of det(A) where A =\n[[1, 6, 1, -4],\n [6, 4, 4, -8],\n [1, 4, -11, 7],\n [-4, -8, 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" } ]
820
MATH
[ { "content": "What is the determinant of the matrix:\n[[-11, -5, 11, 8],\n [0, -7, 9, -7],\n [0, 0, 9, -6],\n [0, 0, 0, 1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
693
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[12, 11, 9, 11],\n [0, 4, 12, -9],\n [0, 0, 12, -1],\n [0, 0, 0, -10]]\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[[3, 9, -8, -6],\n [0, -9, 8, -2],\n [0, 0, -3, -9],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
595
MATH
[ { "content": "Compute |A| for the matrix A =\n[[10, 11, 1, -9],\n [5, 7, 5, 4],\n [-11, -1, 11, 3],\n [-7, -1, 11, -5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
872
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-2, -6, -3, 1],\n [0, -4, -2, 6],\n [0, 0, -8, -7],\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" } ]
552
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-3, 2, 4, -1],\n [2, 12, 8, -5],\n [4, 8, -3, 2],\n [-1, -5, 2, -1]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
319
MATH
[ { "content": "What is the determinant of the matrix:\n[[4, 3, -6, 1],\n [3, 6, 1, -2],\n [-6, 1, 1, 6],\n [1, -2, 6, -6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
997
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-2, 0, -10, -10],\n [0, 7, 1, 8],\n [-10, 1, 10, 4],\n [-10, 8, 4, 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" } ]
362
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-4, -10, -1, 3],\n [2, -12, -1, -12],\n [-3, -8, -4, 12],\n [-7, -6, -12, 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" } ]
180
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-4, -7, 6, 7],\n [-11, -6, 5, 10],\n [12, 9, 8, -10],\n [-4, 2, 2, 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" } ]
688
MATH
[ { "content": "Compute |A| for the matrix A =\n[[3, 9, -3, 7],\n [0, -10, 9, 12],\n [0, 0, -7, 0],\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" } ]
50
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, 4, 4, 0],\n [4, -6, 8, 9],\n [4, 8, -4, 1],\n [0, 9, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
118
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, 0, 2, -3],\n [0, 0, -4, -6],\n [2, -4, -6, 4],\n [-3, -6, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
528
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, -12, 9, 0],\n [-6, 4, 5, -2],\n [-4, 1, 4, 9],\n [2, -5, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
206
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-1, -7, 0, -6],\n [-11, 5, 5, 8],\n [10, -12, 1, -4],\n [-2, -6, 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" } ]
808
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, 9, -6, 0],\n [9, -11, 2, -4],\n [-6, 2, 5, -5],\n [0, -4, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
888
MATH
[ { "content": "Compute |A| for the matrix A =\n[[1, 2, 0, 6],\n [2, -10, -2, -4],\n [0, -2, 0, -2],\n [6, -4, -2, 3]]\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": "Determine the value of det(A) where A =\n[[-6, 0, -2, 6],\n [0, 5, -7, -2],\n [-2, -7, -11, 4],\n [6, -2, 4, -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" } ]
536
MATH
[ { "content": "What is the determinant of the matrix:\n[[-7, 7, -6, 10],\n [7, -7, -4, 2],\n [-6, -4, 5, 2],\n [10, 2, 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" } ]
384
MATH
[ { "content": "Compute |A| for the matrix A =\n[[2, -1, -11, 6],\n [0, 9, -5, 1],\n [0, 0, -10, 9],\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" } ]
180
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, 1, 3, -2],\n [1, 6, -7, 9],\n [3, -7, -6, 2],\n [-2, 9, 2, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
155
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, 10, -2, 4],\n [10, 0, 3, 0],\n [-2, 3, 10, 6],\n [4, 0, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
304
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, -11, 5, 0],\n [0, -3, -1, 4],\n [0, 0, -1, 5],\n [0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
108
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-7, -10, -1, 6],\n [-10, 12, 2, 3],\n [-1, 2, -10, -4],\n [6, 3, -4, 3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
339
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-10, 1, -3, -3],\n [0, -1, 8, 3],\n [0, 0, -12, 6],\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" } ]
920
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-4, 7, 9, 3],\n [7, 11, 5, -10],\n [4, -7, -5, -6],\n [2, 9, 2, 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" } ]
327
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-8, -4, -2, 2],\n [-4, -11, 0, 1],\n [-2, 0, 5, 8],\n [2, 1, 8, -2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
344
MATH
[ { "content": "Compute |A| for the matrix A =\n[[10, 8, 10, 12],\n [0, -4, 1, -9],\n [0, 0, 12, -8],\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" } ]
280
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-8, -1, -12, -2],\n [0, -11, 11, 6],\n [0, 0, -12, 7],\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" } ]
168
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, 7, -2, 5],\n [0, -1, 3, 6],\n [0, 0, 6, -11],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
208
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, 0, 4, -5],\n [0, 5, -2, 2],\n [4, -2, -4, -6],\n [-5, 2, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
240
MATH
[ { "content": "What is the determinant of the matrix:\n[[4, 4, 12, -6],\n [-12, -8, -2, 6],\n [4, 8, 5, -6],\n [3, 1, 5, 6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
552
MATH
[ { "content": "Compute |A| for the matrix A =\n[[8, 9, 4, -12],\n [9, -10, 2, 5],\n [-6, 8, 9, 8],\n [-6, 2, 7, 5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
403
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 2, -6, 5],\n [0, -10, -3, -7],\n [0, 0, 7, 6],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
800
MATH
[ { "content": "What is the determinant of the matrix:\n[[-1, -6, 10, 9],\n [-1, 2, 2, -8],\n [4, -11, 7, 0],\n [11, 2, -12, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
306
MATH
[ { "content": "Determine the value of det(A) where A =\n[[5, 3, 6, -8],\n [3, -6, -6, 0],\n [6, -6, -2, -8],\n [-8, 0, -8, -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" } ]
34
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 9, 11, -1],\n [0, 1, 4, -5],\n [0, 0, 11, 1],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
55
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-5, 8, 4, -5],\n [8, 1, 2, 0],\n [4, 2, -12, 2],\n [-5, 0, 2, -11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
356
MATH
[ { "content": "Compute |A| for the matrix A =\n[[5, 3, -2, -2],\n [3, -5, 0, 6],\n [-2, 0, 7, 6],\n [-2, 6, 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" } ]
334
MATH
[ { "content": "What is the determinant of the matrix:\n[[0, -6, 3, -10],\n [7, 10, 6, 9],\n [11, -11, -8, 7],\n [-5, -10, 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" } ]
227
MATH
[ { "content": "Determine the value of det(A) where A =\n[[0, 4, -3, 3],\n [4, 2, 2, 2],\n [-3, 2, -7, -4],\n [3, 2, -4, -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" } ]
920
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, -2, -8, 4],\n [0, -2, 12, 8],\n [0, 0, 4, -5],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
360
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, -11, -4, 2],\n [10, 7, 6, 8],\n [-5, 3, -3, 7],\n [-9, -6, -12, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
31
MATH
[ { "content": "What is the determinant of the matrix:\n[[1, 9, -4, -2],\n [0, 1, 12, -5],\n [0, 0, 6, -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" } ]
12
MATH
[ { "content": "What is the determinant of the matrix:\n[[7, 6, 2, -7],\n [6, -6, 5, -7],\n [2, 5, -8, 9],\n [-7, -7, 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" } ]
469
MATH
[ { "content": "Determine the value of det(A) where A =\n[[7, 4, 9, -3],\n [9, 0, 5, -6],\n [10, -1, -2, -11],\n [0, 0, 3, 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" } ]
255
MATH
[ { "content": "Determine the value of det(A) where A =\n[[11, -4, -6, -6],\n [-4, -4, -4, 10],\n [-6, -4, 10, -5],\n [-6, 10, -5, -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" } ]
140
MATH
[ { "content": "Compute |A| for the matrix A =\n[[1, -4, 4, -2],\n [-4, 7, 9, 3],\n [4, 9, -9, 6],\n [-2, 3, 6, 6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
89
MATH
[ { "content": "What is the determinant of the matrix:\n[[8, 0, 1, -3],\n [0, -3, -12, -2],\n [0, 0, 9, -3],\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" } ]
728
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, 0, 3, -1],\n [0, 2, -8, -6],\n [0, 0, 2, -4],\n [0, 0, 0, 12]]\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[[-7, 11, 5, 0],\n [-9, -10, 6, 6],\n [-12, 10, 0, 5],\n [1, 5, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
26
MATH
[ { "content": "Determine the value of det(A) where A =\n[[1, 8, -2, 2],\n [8, -3, -3, 8],\n [-2, -3, -9, -1],\n [2, 8, -1, 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" } ]
321
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 7, 9, -6],\n [-9, 9, 9, 7],\n [-11, 7, 11, -10],\n [2, 1, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
390
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-3, 11, 9, 0],\n [-3, -1, 10, 7],\n [0, -6, 12, 6],\n [12, -6, 1, 10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
702
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-3, -6, -6, -9],\n [-6, 9, -2, -9],\n [-6, -2, 2, 6],\n [-9, -9, 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" } ]
762
MATH
[ { "content": "What is the determinant of the matrix:\n[[1, -5, -5, 6],\n [0, 11, 5, -10],\n [0, 0, 9, -10],\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" } ]
505
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, -1, -8, 1],\n [-1, -1, -9, -2],\n [-7, -1, -3, 4],\n [8, 3, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
368
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-11, 9, 2, -6],\n [-3, 4, 3, -6],\n [-8, 6, 5, -6],\n [-6, 12, 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" } ]
771
MATH
[ { "content": "What is the determinant of the matrix:\n[[9, 2, 1, 6],\n [0, -6, 12, 5],\n [-4, -8, 8, -5],\n [-5, -11, 3, 3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
640
MATH
[ { "content": "Compute |A| for the matrix A =\n[[5, -6, 4, 1],\n [0, 7, -1, -6],\n [0, 0, -11, -11],\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" } ]
310
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, 5, -2, -9],\n [0, 2, 1, 8],\n [0, 0, -7, -2],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
888
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-12, 2, 0, -2],\n [2, 4, -2, -10],\n [0, -2, -9, -5],\n [-2, -10, -5, -8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
292
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, -9, -3, 1],\n [0, 5, 10, -1],\n [0, 0, 12, 9],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
700
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, -4, 6, 0],\n [-4, 10, -4, -10],\n [6, -4, 7, 7],\n [0, -10, 7, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
312
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, 8, 8, -4],\n [8, -4, -6, 3],\n [8, -6, -8, -2],\n [-4, 3, -2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
384
MATH
[ { "content": "Compute |A| for the matrix A =\n[[1, 1, 4, -1],\n [4, 0, -2, 7],\n [8, 8, 3, 6],\n [-4, -3, -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" } ]
867
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, -4, 4, 11],\n [1, 11, -10, 7],\n [-9, 12, 12, -12],\n [-6, -1, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
90
MATH
[ { "content": "Determine the value of det(A) where A =\n[[11, -3, -12, -4],\n [2, -5, 9, -4],\n [-8, -2, 12, -2],\n [7, -5, 12, -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" } ]
282
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, 5, -7, -9],\n [-4, -2, 4, -3],\n [-8, 9, -8, 3],\n [5, 6, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
737
MATH
[ { "content": "What is the determinant of the matrix:\n[[3, 1, 10, 7],\n [1, -11, -2, -10],\n [10, -2, -5, 0],\n [7, -10, 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" } ]
773
MATH
[ { "content": "What is the determinant of the matrix:\n[[1, -6, 9, 2],\n [-12, 5, 3, -7],\n [7, -9, 10, -4],\n [8, -3, -5, 12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
748
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-10, -2, 8, 2],\n [-2, 9, 4, 8],\n [8, 4, 3, 2],\n [2, 8, 2, 9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
570
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, 6, 2, -7],\n [0, -12, -7, -10],\n [0, 0, 11, 8],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
664
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, 8, 11, 2],\n [-2, -2, 7, 11],\n [0, 1, 8, 6],\n [-10, -10, -10, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
872
MATH