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[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, 7, 11, -5],\n [11, -4, -8, -7],\n [0, 8, 6, -12],\n [-11, -10, -4, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
732
MATH
[ { "content": "What is the determinant of the matrix:\n[[-11, 8, 6, -4],\n [8, 1, 6, -3],\n [6, 6, 5, -6],\n [-4, -3, -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" } ]
601
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, -10, 3, 3],\n [-8, -1, 12, 2],\n [9, -5, 0, -1],\n [-5, -2, 5, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
81
MATH
[ { "content": "What is the determinant of the matrix:\n[[11, 1, 1, 8],\n [0, -4, -6, 8],\n [0, 0, 3, 0],\n [0, 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" } ]
528
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-7, 12, -11, -3],\n [0, 4, 7, -11],\n [0, 0, 1, 0],\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" } ]
664
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, -4, 3, 3],\n [0, -9, 9, -12],\n [0, 0, -10, -7],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
200
MATH
[ { "content": "Determine the value of det(A) where A =\n[[1, 12, 7, -4],\n [0, -11, 3, 11],\n [0, 0, -6, -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" } ]
528
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, 10, -2, -4],\n [0, -5, 12, -1],\n [0, 0, 11, -7],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
535
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-3, -5, 10, 5],\n [0, 9, -1, 12],\n [0, 0, 5, -12],\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" } ]
945
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, -3, 5, -4],\n [0, 6, 2, 10],\n [0, 0, -11, -2],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
664
MATH
[ { "content": "What is the determinant of the matrix:\n[[0, -4, -5, 0],\n [-4, 12, 0, -6],\n [-5, 0, -3, 3],\n [0, -6, 3, -5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
24
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, 1, 2, 4],\n [1, 3, -5, -4],\n [2, -5, -12, 6],\n [4, -4, 6, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
852
MATH
[ { "content": "Compute |A| for the matrix A =\n[[1, 4, 2, 4],\n [0, -6, -4, -8],\n [0, 0, -4, 11],\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" } ]
168
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, 1, 0, 4],\n [-9, 4, -1, -5],\n [-1, -9, 11, -2],\n [0, -1, -10, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
738
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-9, -6, -1, 8],\n [0, 1, -4, -9],\n [0, 0, -9, 4],\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" } ]
324
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, 0, -6, -2],\n [0, 7, -1, 6],\n [0, 0, 11, -4],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
228
MATH
[ { "content": "Determine the value of det(A) where A =\n[[1, 6, 10, 12],\n [0, 1, 3, 1],\n [5, -8, 3, 2],\n [-9, 12, -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" } ]
769
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, 4, 6, -9],\n [4, -6, 3, -2],\n [6, 3, 9, -10],\n [-9, -2, -10, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
441
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-11, 4, 6, -4],\n [4, -1, 4, 3],\n [6, 4, -8, -2],\n [-4, 3, -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" } ]
44
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-2, -1, 8, 6],\n [-3, -7, -7, -3],\n [-11, -2, 2, -7],\n [12, -6, -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" } ]
753
MATH
[ { "content": "Determine the value of det(A) where A =\n[[2, 6, 0, -6],\n [0, -12, -11, -12],\n [0, 0, 12, -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" } ]
408
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, 10, 7, -3],\n [3, 12, -11, -5],\n [-2, -2, 2, 2],\n [-12, -8, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
828
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, 8, -2, 1],\n [0, 11, 8, 8],\n [0, 0, 11, 2],\n [0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
100
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, 0, -4, -11],\n [0, 10, 4, 3],\n [0, 0, 4, 2],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
280
MATH
[ { "content": "What is the determinant of the matrix:\n[[11, 6, -12, 1],\n [6, -2, -2, -2],\n [-12, -2, 9, 9],\n [1, -2, 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" } ]
558
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, -3, 5, 0],\n [-3, -4, -3, 2],\n [5, -3, -3, 0],\n [0, 2, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
980
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, 0, 0, 0],\n [0, -12, 3, 5],\n [0, 0, -9, -12],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
920
MATH
[ { "content": "What is the determinant of the matrix:\n[[-1, 3, -2, -1],\n [0, 5, 11, -1],\n [0, 0, 1, 8],\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" } ]
960
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, 5, 1, -1],\n [-7, 0, -5, 5],\n [-7, -4, -3, 12],\n [-10, -7, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
474
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, -6, 11, -8],\n [-8, -2, 6, -7],\n [11, 9, -2, -2],\n [0, -6, 5, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
16
MATH
[ { "content": "Compute |A| for the matrix A =\n[[9, -11, 2, -12],\n [-7, 2, 12, 0],\n [2, -1, -6, 3],\n [10, -1, -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" } ]
244
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-6, 0, 6, 4],\n [0, -7, 11, -3],\n [6, 11, 4, -4],\n [4, -3, -4, 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" } ]
618
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-11, -9, 3, 4],\n [0, 7, -12, -9],\n [0, 0, -6, 10],\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" } ]
772
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, 4, -7, -4],\n [-7, 0, 0, -10],\n [-2, 9, -5, 4],\n [-1, 6, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
186
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-4, -12, 11, -6],\n [-2, -3, -3, 9],\n [-8, 10, -11, 0],\n [7, 0, 1, -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" } ]
864
MATH
[ { "content": "Compute |A| for the matrix A =\n[[11, -5, -7, 0],\n [-5, 1, 3, -3],\n [-7, 3, 7, 6],\n [0, -3, 6, -12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
756
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, -4, -7, -4],\n [0, 2, -10, 3],\n [0, 0, 9, 10],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
136
MATH
[ { "content": "Compute |A| for the matrix A =\n[[1, -8, -9, -6],\n [0, -9, 1, 7],\n [0, 0, -6, -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" } ]
270
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, -3, 0, 2],\n [-3, 3, -3, -4],\n [0, -3, -10, -2],\n [2, -4, -2, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
587
MATH
[ { "content": "Determine the value of det(A) where A =\n[[6, 2, 10, 0],\n [0, -3, -12, 8],\n [0, 0, -3, 12],\n [0, 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" } ]
730
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, -11, 12, -2],\n [-12, 2, 3, 8],\n [9, -4, -7, 9],\n [-1, 2, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
184
MATH
[ { "content": "What is the determinant of the matrix:\n[[-9, -1, -6, -10],\n [-1, -2, 8, -2],\n [-6, 8, 3, 5],\n [-10, -2, 5, -7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
622
MATH
[ { "content": "What is the determinant of the matrix:\n[[-6, 8, 5, -10],\n [0, 6, -8, -10],\n [0, 0, 12, 12],\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" } ]
568
MATH
[ { "content": "What is the determinant of the matrix:\n[[6, -8, -8, 0],\n [-8, -3, -7, -2],\n [-8, -7, -7, -6],\n [0, -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" } ]
376
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-8, -6, -4, -2],\n [4, 9, -4, -3],\n [11, -9, -12, -1],\n [6, -8, -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" } ]
148
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, 10, 1, -8],\n [0, 8, -9, -7],\n [0, 0, 10, -1],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
720
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-12, 12, 11, -10],\n [0, -11, -3, -2],\n [0, 0, 3, -5],\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" } ]
168
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-3, 2, 5, -8],\n [1, -5, -1, -9],\n [-3, -10, -1, -7],\n [-4, 4, 9, 4]]\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": "Determine the value of det(A) where A =\n[[4, -7, 11, 11],\n [0, -4, 12, 10],\n [0, 0, 2, 5],\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" } ]
712
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-11, 4, -2, -4],\n [4, 6, -8, 4],\n [-2, -8, 9, 1],\n [-4, 4, 1, 12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
698
MATH
[ { "content": "Compute |A| for the matrix A =\n[[5, 4, -7, 6],\n [-6, -2, 8, 12],\n [-11, 6, 11, 10],\n [3, -5, 12, -5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
248
MATH
[ { "content": "Compute |A| for the matrix A =\n[[11, -2, -4, 4],\n [-2, 12, 6, -1],\n [-4, 6, -11, -4],\n [4, -1, -4, 11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
125
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-3, 2, 8, -8],\n [2, -6, -6, 5],\n [8, -6, 7, 1],\n [-8, 5, 1, -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" } ]
555
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-2, -11, 0, -2],\n [0, 5, 11, 12],\n [0, 0, -1, -11],\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" } ]
970
MATH
[ { "content": "What is the determinant of the matrix:\n[[-1, 0, -2, 3],\n [5, 3, 11, -4],\n [2, -3, 6, -5],\n [-1, 9, 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" } ]
468
MATH
[ { "content": "Compute |A| for the matrix A =\n[[6, 5, 0, -2],\n [0, 5, 4, 12],\n [0, 0, 3, -7],\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" } ]
910
MATH
[ { "content": "What is the determinant of the matrix:\n[[6, 6, -6, 7],\n [6, -7, -5, -8],\n [-6, -5, 5, 6],\n [7, -8, 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" } ]
100
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, 4, 0, 0],\n [4, 8, 0, -1],\n [0, 0, -6, 4],\n [0, -1, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
832
MATH
[ { "content": "What is the determinant of the matrix:\n[[-7, 2, -4, -11],\n [-3, 3, -12, -4],\n [-6, -3, 11, 5],\n [11, 11, -7, 12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
874
MATH
[ { "content": "What is the determinant of the matrix:\n[[11, 4, 1, -3],\n [-1, 10, 5, 2],\n [7, 8, 5, -7],\n [-12, -4, 6, -11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
976
MATH
[ { "content": "Compute |A| for the matrix A =\n[[5, 3, -8, 8],\n [-3, 1, 11, 3],\n [-4, 5, -9, -1],\n [8, -4, 8, -10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
818
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-9, -5, -2, 1],\n [-5, 12, -6, -8],\n [-2, -6, -12, 0],\n [1, -8, 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" } ]
268
MATH
[ { "content": "Compute |A| for the matrix A =\n[[0, 4, -1, -5],\n [-1, -9, 5, -8],\n [-3, 10, 6, -4],\n [-10, -5, -11, 10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
730
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-6, -7, 2, 5],\n [-7, 12, -4, -5],\n [2, -4, 1, -5],\n [5, -5, -5, -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" } ]
35
MATH
[ { "content": "What is the determinant of the matrix:\n[[-7, -7, 12, 5],\n [0, -4, 0, 4],\n [0, 0, -7, 4],\n [0, 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" } ]
216
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, -10, 9, -3],\n [0, -4, 6, -11],\n [0, 0, -6, 5],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
640
MATH
[ { "content": "What is the determinant of the matrix:\n[[-1, -12, 2, 3],\n [0, -12, -5, 1],\n [0, 0, -12, -12],\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" } ]
560
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-2, 2, -5, 1],\n [0, 8, -2, -2],\n [0, 0, -5, -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" } ]
800
MATH
[ { "content": "Determine the value of det(A) where A =\n[[2, 1, 4, -4],\n [1, 11, 4, 0],\n [4, 4, -6, -6],\n [-4, 0, -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" } ]
100
MATH
[ { "content": "What is the determinant of the matrix:\n[[0, -4, 0, 4],\n [-4, -8, 8, 0],\n [0, 8, 5, 0],\n [4, 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" } ]
824
MATH
[ { "content": "What is the determinant of the matrix:\n[[3, 5, 11, -2],\n [0, -4, 1, 2],\n [0, 0, 2, -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" } ]
832
MATH
[ { "content": "What is the determinant of the matrix:\n[[5, 8, 2, 0],\n [8, -6, 0, -4],\n [2, 0, 3, 10],\n [0, -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" } ]
924
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, -5, 7, 4],\n [-5, 12, -2, 2],\n [7, -2, -7, -3],\n [4, 2, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
697
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, 10, 12, -12],\n [0, -3, 11, 11],\n [0, 0, -11, 0],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
459
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, -3, -6, -5],\n [-3, 4, 6, 8],\n [-6, 6, 7, 0],\n [-5, 8, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
873
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[12, 12, 1, -4],\n [0, -11, -7, -7],\n [0, 0, -9, 11],\n [0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
880
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-1, 6, 2, -5],\n [-6, -9, 1, 2],\n [-10, 0, -11, 6],\n [10, -3, -10, 0]]\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[[8, -9, -12, 12],\n [0, -11, 5, -10],\n [0, 0, -5, 1],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
440
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, -3, 2, -2],\n [-3, 8, 5, 10],\n [2, 5, -8, 4],\n [-2, 10, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
11
MATH
[ { "content": "Compute |A| for the matrix A =\n[[1, -2, 7, 11],\n [0, 6, -10, -9],\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" } ]
84
MATH
[ { "content": "Determine the value of det(A) where A =\n[[5, -9, 2, 12],\n [7, 5, -7, 7],\n [12, -4, -5, -5],\n [-7, -3, -2, -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" } ]
344
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, 10, 8, -8],\n [0, 11, 10, 2],\n [0, 0, 5, 5],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
680
MATH
[ { "content": "Compute |A| for the matrix A =\n[[12, -5, -4, -6],\n [-5, 0, 8, -4],\n [-4, 8, -6, 6],\n [-6, -4, 6, -4]]\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": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, -9, -6, -9],\n [10, 2, 7, -4],\n [-3, 10, -2, -9],\n [-4, 7, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
386
MATH
[ { "content": "Compute |A| for the matrix A =\n[[11, 6, -1, 8],\n [6, 7, -2, -8],\n [-1, -2, -12, 4],\n [8, -8, 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" } ]
304
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-10, 4, 12, 1],\n [-8, 0, 1, -3],\n [-11, -8, -3, 3],\n [9, 5, -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" } ]
47
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-6, -5, 10, 0],\n [0, -5, 0, -4],\n [0, 0, -11, -11],\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" } ]
310
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, 4, -3, -9],\n [-6, 9, 1, -1],\n [-11, -4, -3, 1],\n [-8, -4, -8, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
694
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, 11, 4, 7],\n [-11, -4, 10, -3],\n [11, 3, 12, -10],\n [1, 2, 11, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
759
MATH
[ { "content": "What is the determinant of the matrix:\n[[-6, -10, -11, 4],\n [0, -5, -1, -7],\n [0, 0, -3, -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" } ]
90
MATH
[ { "content": "Compute |A| for the matrix A =\n[[3, -1, 2, 4],\n [3, -11, -6, -3],\n [-2, 10, -8, 0],\n [-9, -7, 6, 4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
432
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, 6, 4, -10],\n [0, 2, -5, 11],\n [0, 0, 6, -3],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
144
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, 8, -2, -3],\n [8, -7, 6, 6],\n [-2, 6, -6, -4],\n [-3, 6, -4, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
566
MATH
[ { "content": "What is the determinant of the matrix:\n[[11, 2, 2, -4],\n [2, 10, 1, -4],\n [2, 1, 6, -4],\n [-4, -4, -4, -11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
965
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, -10, -9, -12],\n [0, -3, -10, -12],\n [0, 0, 3, -10],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
676
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-6, -3, 0, 4],\n [-3, 9, 4, -6],\n [0, 4, 10, 4],\n [4, -6, 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" } ]
960
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, -2, -3, 9],\n [5, -5, 7, 11],\n [-11, 2, 9, -8],\n [12, 10, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
133
MATH
[ { "content": "Determine the value of det(A) where A =\n[[8, -1, -6, -1],\n [0, 12, -1, -4],\n [0, 0, -3, 10],\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" } ]
16
MATH
[ { "content": "Compute |A| for the matrix A =\n[[8, 4, -4, -2],\n [4, -2, -4, 3],\n [-4, -4, -3, -8],\n [-2, 3, -8, 10]]\nRound to the nearest integer, then take the result modulo 1000.\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[[-2, 1, -1, 8],\n [0, -12, 3, -3],\n [0, 0, 3, -8],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
640
MATH