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[ { "content": "Compute |A| for the matrix A =\n[[1, 10, 4],\n [0, -8, -5],\n [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" } ]
968
MATH
[ { "content": "What is the determinant of the matrix:\n[[9, 0, -1],\n [0, -8, 2],\n [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" } ]
856
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 8, 1],\n [4, -3, 2],\n [2, -2, 1]]\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[[-5, 4, 4],\n [-3, 6, 2],\n [2, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
908
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-10, -9, 0],\n [-9, -4, 8],\n [-9, 6, 5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
923
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-7, -10, 7],\n [-9, -10, -8],\n [-5, -9, -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" } ]
521
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[0, 1, 4],\n [1, -4, -6],\n [4, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
11
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-7, -5, 9],\n [0, 3, 2],\n [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" } ]
979
MATH
[ { "content": "Compute |A| for the matrix A =\n[[10, 8, 3],\n [-7, 7, -7],\n [10, 5, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
357
MATH
[ { "content": "Determine the value of det(A) where A =\n[[7, -1, 2],\n [0, -9, -5],\n [0, 0, -5]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
315
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, 5, -9],\n [5, -10, 5],\n [-9, 5, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
480
MATH
[ { "content": "Determine the value of det(A) where A =\n[[6, 0, -1],\n [0, -10, -2],\n [-1, -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" } ]
686
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-5, 9, 10],\n [0, -5, 1],\n [10, 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" } ]
745
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-10, -8, 8],\n [5, -4, -8],\n [-1, -2, -2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
824
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, -7, -8],\n [0, 2, -5],\n [0, 0, -5]]\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, -8, -9],\n [0, 6, 3],\n [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" } ]
964
MATH
[ { "content": "Compute |A| for the matrix A =\n[[3, -1, 10],\n [6, -10, -6],\n [4, -1, -8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
538
MATH
[ { "content": "What is the determinant of the matrix:\n[[4, 8, -9],\n [7, 3, -7],\n [-4, 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" } ]
30
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, -2, -2],\n [10, 2, -4],\n [8, -2, 0]]\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[[6, -4, -8],\n [0, -2, -2],\n [0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
60
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-3, -1, 7],\n [-6, 10, -6],\n [-9, 10, -5]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
156
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, -8, -8],\n [0, -1, 5],\n [0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
960
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-7, 6, 1],\n [6, 6, 3],\n [1, 3, -3]]\nRound to the nearest integer, then take the result modulo 1000.\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[[2, 0, -4],\n [0, -10, 4],\n [-4, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
168
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-6, 8, -6],\n [-6, 8, 10],\n [-6, 2, 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" } ]
424
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 3, 2],\n [0, 1, -4],\n [0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
985
MATH
[ { "content": "What is the determinant of the matrix:\n[[-7, -6, 10],\n [-8, -8, 0],\n [5, 7, 0]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
840
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, 6, 8],\n [6, -10, -2],\n [8, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
306
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-9, -8, -3],\n [-8, 1, -8],\n [-3, -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" } ]
672
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, -4, 5],\n [0, -6, 3],\n [0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
216
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-7, -4, 7],\n [0, 5, -10],\n [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" } ]
720
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, -4, -2],\n [5, -3, 2],\n [9, 6, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
630
MATH
[ { "content": "What is the determinant of the matrix:\n[[-10, -3, 2],\n [0, 8, 10],\n [0, 0, -4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
320
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-10, 0, 7],\n [0, 4, -6],\n [7, -6, -2]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
244
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-5, 2, -6],\n [2, 10, 4],\n [-6, 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" } ]
56
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-2, -6, 7],\n [-6, -6, 2],\n [7, 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" } ]
278
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-5, 3, -7],\n [0, -2, -4],\n [-3, -9, 6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
318
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, 1, 10],\n [0, 5, 8],\n [0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
965
MATH
[ { "content": "Determine the value of det(A) where A =\n[[7, 4, -1],\n [0, -1, 2],\n [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" } ]
930
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, 0, -6],\n [0, 7, 0],\n [-6, 0, -9]]\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, -8, 9],\n [0, 4, 4],\n [0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
240
MATH
[ { "content": "Compute |A| for the matrix A =\n[[4, 0, 4],\n [0, 9, -8],\n [4, -8, 3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
708
MATH
[ { "content": "Compute |A| for the matrix A =\n[[3, -7, -4],\n [-8, -2, 0],\n [3, -8, -5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
30
MATH
[ { "content": "Determine the value of det(A) where A =\n[[8, 4, -4],\n [4, 6, -7],\n [-4, -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" } ]
736
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-6, -4, 2],\n [-4, 2, -4],\n [2, -4, 10]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
872
MATH
[ { "content": "What is the determinant of the matrix:\n[[7, 7, -1],\n [4, -4, -6],\n [10, 1, -10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
138
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-5, -8, -3],\n [0, -10, 2],\n [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" } ]
250
MATH
[ { "content": "What is the determinant of the matrix:\n[[3, 6, 1],\n [0, -1, 0],\n [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" } ]
27
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, -7, 4],\n [-7, 10, -2],\n [4, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
546
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, 0, 9],\n [0, -2, -4],\n [0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
90
MATH
[ { "content": "What is the determinant of the matrix:\n[[6, -3, -3],\n [0, 9, 6],\n [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" } ]
540
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-6, -8, -1],\n [-8, 0, 4],\n [-1, 4, 2]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
32
MATH
[ { "content": "What is the determinant of the matrix:\n[[-10, 8, -4],\n [0, 3, -1],\n [-3, -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" } ]
28
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 3, 2],\n [3, -10, 4],\n [2, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
216
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, -1, 8],\n [-1, -7, 2],\n [8, 2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
476
MATH
[ { "content": "What is the determinant of the matrix:\n[[5, -7, -1],\n [0, -9, 7],\n [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" } ]
45
MATH
[ { "content": "Determine the value of det(A) where A =\n[[6, 9, -8],\n [3, -3, 0],\n [0, 3, 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" } ]
928
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, -6, -3],\n [-6, -6, 0],\n [-3, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
30
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, -3, -6],\n [-3, -10, -9],\n [-6, -9, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
308
MATH
[ { "content": "What is the determinant of the matrix:\n[[-1, 1, 10],\n [0, 4, -4],\n [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" } ]
992
MATH
[ { "content": "Compute |A| for the matrix A =\n[[5, 5, -9],\n [0, -6, 10],\n [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" } ]
970
MATH
[ { "content": "Determine the value of det(A) where A =\n[[5, 0, 5],\n [0, 7, -8],\n [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" } ]
140
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, -3, 7],\n [0, 2, 1],\n [0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
140
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, -4, -1],\n [-10, 1, -4],\n [7, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
914
MATH
[ { "content": "Determine the value of det(A) where A =\n[[6, 6, -2],\n [0, -9, 3],\n [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" } ]
540
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, -8, 5],\n [-1, -9, 2],\n [3, 8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
175
MATH
[ { "content": "What is the determinant of the matrix:\n[[-8, -7, -1],\n [0, -4, -2],\n [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" } ]
64
MATH
[ { "content": "What is the determinant of the matrix:\n[[1, -4, 0],\n [6, -2, -9],\n [5, 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" } ]
9
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, 7, -10],\n [5, 8, -6],\n [3, -8, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
997
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, 5, -3],\n [0, 1, 3],\n [0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
930
MATH
[ { "content": "Determine the value of det(A) where A =\n[[2, 5, 2],\n [1, 0, -8],\n [2, 6, 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" } ]
978
MATH
[ { "content": "Determine the value of det(A) where A =\n[[2, -1, -9],\n [-4, 7, 3],\n [5, 3, 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" } ]
490
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, 1, -4],\n [1, -9, -3],\n [-4, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
317
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, -9, 6],\n [0, 3, 8],\n [0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
976
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-5, 7, -3],\n [0, 1, 7],\n [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" } ]
20
MATH
[ { "content": "Determine the value of det(A) where A =\n[[5, -7, -3],\n [0, 7, -10],\n [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" } ]
720
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, 2, -3],\n [-5, -6, 8],\n [1, -10, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
710
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, 9, -2],\n [0, 1, -2],\n [3, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
968
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, -3, -3],\n [5, 1, -10],\n [-8, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
821
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, -7, -10],\n [0, 6, -2],\n [0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
96
MATH
[ { "content": "Compute |A| for the matrix A =\n[[4, 6, 8],\n [6, 2, -6],\n [8, -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" } ]
320
MATH
[ { "content": "Determine the value of det(A) where A =\n[[2, 1, -6],\n [1, 2, 6],\n [-6, 6, -3]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
775
MATH
[ { "content": "Determine the value of det(A) where A =\n[[3, -10, 4],\n [-3, 0, -7],\n [4, 9, -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" } ]
571
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, -8, 8],\n [0, -9, -2],\n [0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
315
MATH
[ { "content": "What is the determinant of the matrix:\n[[4, 0, 0],\n [0, 4, 2],\n [0, 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" } ]
32
MATH
[ { "content": "Compute |A| for the matrix A =\n[[3, -4, -9],\n [-4, -8, 0],\n [-9, 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" } ]
808
MATH
[ { "content": "What is the determinant of the matrix:\n[[7, 9, 4],\n [2, -1, -1],\n [-5, -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" } ]
870
MATH
[ { "content": "What is the determinant of the matrix:\n[[-7, 2, 1],\n [10, -10, -10],\n [-1, -2, 7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
480
MATH
[ { "content": "What is the determinant of the matrix:\n[[-10, -7, 6],\n [7, 2, 10],\n [4, 6, 9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
785
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-9, -10, -5],\n [0, 3, -9],\n [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" } ]
243
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, -4, -2],\n [-10, 8, -4],\n [0, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
760
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, 8, -6],\n [0, -2, -10],\n [0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
96
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, -7, -8],\n [-8, -2, -2],\n [-3, 10, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
306
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-7, 1, -6],\n [1, 9, 0],\n [-6, 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" } ]
356
MATH
[ { "content": "What is the determinant of the matrix:\n[[9, -2, -4],\n [-2, -4, -4],\n [-4, -4, 8]]? Round to the nearest integer, then express your answer modulo 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[[3, 2, 0],\n [0, -5, 4],\n [0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
955
MATH
[ { "content": "What is the determinant of the matrix:\n[[10, 9, -7],\n [9, 5, -3],\n [9, 7, 8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
593
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-5, 8, 10],\n [2, -2, -7],\n [10, -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" } ]
601
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-7, -6, 6],\n [0, -6, 8],\n [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" } ]
790
MATH
[ { "content": "What is the determinant of the matrix:\n[[10, 1, 4],\n [1, 5, -10],\n [4, -10, -10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
350
MATH