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[ { "content": "What is the determinant of the matrix:\n[[5, 10, -2, 6],\n [0, -10, -8, 2],\n [0, 0, 10, 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" } ]
0
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[12, 4, 8, 0],\n [4, -2, 0, 1],\n [8, 0, 3, -10],\n [0, 1, -10, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
724
MATH
[ { "content": "Determine the value of det(A) where A =\n[[0, 0, -2, 2],\n [0, 2, 0, -2],\n [-2, 0, 2, -6],\n [2, -2, -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" } ]
72
MATH
[ { "content": "What is the determinant of the matrix:\n[[9, 4, -3, 3],\n [4, -10, 5, 2],\n [-3, 5, 2, 2],\n [3, 2, 2, -1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
112
MATH
[ { "content": "What is the determinant of the matrix:\n[[-11, 11, 4, -5],\n [0, 1, 6, -4],\n [-11, 2, 2, 4],\n [-8, 10, 9, 8]]? 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": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, -4, 6, -8],\n [-4, -8, 4, 6],\n [6, 4, -8, 4],\n [-8, 6, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
152
MATH
[ { "content": "Compute |A| for the matrix A =\n[[10, -8, -4, 2],\n [-8, -6, 0, -10],\n [-4, 0, 6, 0],\n [2, -10, 0, 0]]\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[[10, -5, -10, 11],\n [0, 9, -4, 7],\n [0, 0, 12, -9],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
120
MATH
[ { "content": "What is the determinant of the matrix:\n[[6, -7, 4, -8],\n [1, -8, -7, 11],\n [10, -1, -4, 3],\n [9, 8, 5, -5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
740
MATH
[ { "content": "Compute |A| for the matrix A =\n[[4, 4, -2, -9],\n [0, 10, -8, -12],\n [0, 0, 4, -4],\n [0, 0, 0, -10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
400
MATH
[ { "content": "What is the determinant of the matrix:\n[[-1, 8, -9, -6],\n [7, 0, -12, 12],\n [-1, 8, 9, -1],\n [-2, -10, 11, 0]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
314
MATH
[ { "content": "What is the determinant of the matrix:\n[[0, -11, 2, 1],\n [10, -9, -2, -9],\n [7, 10, -4, -3],\n [8, 10, -7, 11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
986
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, 5, -2, 10],\n [5, -1, -2, 6],\n [-2, -2, -4, 3],\n [10, 6, 3, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
688
MATH
[ { "content": "Determine the value of det(A) where A =\n[[8, 7, 1, -3],\n [0, 3, -1, -1],\n [0, 0, 9, -2],\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" } ]
648
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, -9, 4, 8],\n [0, 1, -7, -9],\n [0, 0, 2, -2],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
14
MATH
[ { "content": "Compute |A| for the matrix A =\n[[12, -6, 2, 6],\n [-6, -2, 6, 0],\n [2, 6, 7, 5],\n [6, 0, 5, -3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
184
MATH
[ { "content": "Determine the value of det(A) where A =\n[[11, 2, 2, 7],\n [-9, -6, 7, 7],\n [6, 2, 2, -5],\n [3, -5, 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" } ]
411
MATH
[ { "content": "Compute |A| for the matrix A =\n[[10, 7, 2, 0],\n [7, -1, 4, -6],\n [2, 4, 5, 6],\n [0, -6, 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" } ]
664
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, -10, -12, -10],\n [5, 8, 5, -7],\n [6, 4, 1, -9],\n [-3, -10, 10, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
290
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, 3, 12, 3],\n [0, -4, -7, 3],\n [0, 0, 4, -6],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
696
MATH
[ { "content": "What is the determinant of the matrix:\n[[10, 10, 11, 2],\n [0, 12, -4, -7],\n [0, 0, -3, 9],\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" } ]
560
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-8, -6, 0, 2],\n [-6, -8, 6, -2],\n [0, 6, 2, -4],\n [2, -2, -4, -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" } ]
856
MATH
[ { "content": "What is the determinant of the matrix:\n[[10, 8, -12, 12],\n [-5, -3, 10, 1],\n [-5, 11, -7, 3],\n [-12, -2, -3, -6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
816
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, -4, 2, -4],\n [0, -11, -4, 8],\n [0, 0, 12, -4],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
436
MATH
[ { "content": "What is the determinant of the matrix:\n[[-7, -11, 11, -10],\n [-8, 7, 10, 4],\n [-9, 4, 2, 11],\n [10, -11, -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" } ]
144
MATH
[ { "content": "Compute |A| for the matrix A =\n[[4, -7, -12, 5],\n [0, 9, -7, 9],\n [0, 0, -7, -12],\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" } ]
756
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, 4, 0, 3],\n [5, 12, -9, -5],\n [-2, -2, -7, -8],\n [-12, 12, -7, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
322
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-11, 11, 7, 1],\n [11, -8, 5, -4],\n [7, 5, -3, 0],\n [1, -4, 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" } ]
657
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-3, -12, -7, -6],\n [-12, -1, -2, -6],\n [-7, -2, -10, -8],\n [-6, -6, -8, -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" } ]
789
MATH
[ { "content": "What is the determinant of the matrix:\n[[4, 6, -7, -12],\n [-4, -12, 11, -2],\n [-11, -7, 0, 10],\n [3, -1, 9, 3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
226
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-9, 7, 2, 11],\n [0, 2, -7, 0],\n [0, 0, 5, -2],\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" } ]
80
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, 5, 8, 5],\n [5, 4, -4, -8],\n [8, -4, 5, 7],\n [5, -8, 7, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
80
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, -5, 11, 12],\n [0, 8, 9, -12],\n [0, 0, -12, 10],\n [0, 0, 0, 8]]\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[[5, -9, 10, -2],\n [0, 12, 11, 1],\n [0, 0, 5, 3],\n [0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
200
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-5, -3, -3, -1],\n [6, 6, -9, 8],\n [9, -6, 9, -9],\n [1, 9, 8, -4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
387
MATH
[ { "content": "What is the determinant of the matrix:\n[[-12, 0, 6, -8],\n [0, -9, 3, -8],\n [0, 0, 1, 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" } ]
892
MATH
[ { "content": "Compute |A| for the matrix A =\n[[6, 12, -7, 4],\n [-3, -9, -2, 2],\n [-5, 2, -1, 0],\n [-7, -6, 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" } ]
132
MATH
[ { "content": "What is the determinant of the matrix:\n[[-7, 12, 2, 0],\n [0, -11, -6, 9],\n [0, 0, -10, 11],\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" } ]
700
MATH
[ { "content": "What is the determinant of the matrix:\n[[12, 2, -8, -10],\n [2, -6, 0, -12],\n [-8, 0, -1, 2],\n [-10, -12, 2, -6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
720
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, 10, 0, -12],\n [0, -2, 4, 5],\n [0, 0, -12, -11],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
264
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-1, 4, -5, 3],\n [4, -3, -10, -6],\n [-5, -10, -11, 4],\n [3, -6, 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" } ]
117
MATH
[ { "content": "Compute |A| for the matrix A =\n[[1, -1, 7, -2],\n [-1, 3, 0, -2],\n [7, 0, -2, -8],\n [-2, -2, -8, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
955
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, -7, 2, 12],\n [4, 8, 11, 1],\n [12, -11, 9, 11],\n [6, 12, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
380
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, 11, 0, -4],\n [10, 8, 2, 6],\n [12, -2, -6, -5],\n [0, -4, -8, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
416
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-6, -12, -1, -6],\n [-8, 12, -9, -8],\n [-3, -8, -3, 0],\n [-11, -8, 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" } ]
368
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, -6, -6, 7],\n [-6, -12, -2, 4],\n [-6, -2, -6, 2],\n [7, 4, 2, -2]]\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[[-12, 8, -10, -2],\n [8, -11, -10, 2],\n [-10, -10, -8, 0],\n [-2, 2, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
596
MATH
[ { "content": "What is the determinant of the matrix:\n[[-3, -2, 0, 0],\n [10, -9, 6, 0],\n [9, -1, 5, 2],\n [-1, -7, 2, 6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
694
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, -11, 7, -8],\n [0, 7, -4, 1],\n [0, 0, -2, -8],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
120
MATH
[ { "content": "Compute |A| for the matrix A =\n[[11, 11, -4, 9],\n [-11, 5, 2, -9],\n [3, 2, -12, -5],\n [10, 3, 10, 2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
748
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, -2, -8, 2],\n [-2, -5, -4, 5],\n [-8, -4, -12, 4],\n [2, 5, 4, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
456
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, -10, -10, -8],\n [0, -2, 9, 4],\n [0, 0, 2, 11],\n [0, 0, 0, -1]]\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[[-11, -4, -2, -2],\n [-4, 5, 1, -1],\n [-2, 1, 12, 0],\n [-2, -1, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
166
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, 2, -2, 6],\n [2, -12, 6, -5],\n [-2, 6, 4, 0],\n [6, -5, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
4
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, 0, 4, 3],\n [0, -4, -2, -7],\n [4, -2, 9, 3],\n [3, -7, 3, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
670
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, 3, -11, -3],\n [7, 3, 5, -11],\n [-3, 12, 9, -8],\n [8, -11, 7, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
85
MATH
[ { "content": "Determine the value of det(A) where A =\n[[2, -1, -7, -8],\n [0, -7, 9, -8],\n [0, 0, 1, -2],\n [0, 0, 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" } ]
832
MATH
[ { "content": "Determine the value of det(A) where A =\n[[3, -6, -7, 2],\n [-6, -8, 8, -6],\n [-7, 8, 10, 0],\n [2, -6, 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" } ]
988
MATH
[ { "content": "What is the determinant of the matrix:\n[[12, -11, -2, -2],\n [0, 10, 4, -3],\n [0, 0, 3, -7],\n [0, 0, 0, -9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
760
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-12, 4, 3, -2],\n [4, 2, -4, -2],\n [3, -4, -3, 4],\n [-2, -2, 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" } ]
296
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, -10, -9, -10],\n [-3, -6, 4, -8],\n [8, -10, 2, -5],\n [5, 3, 2, -6]]\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[[-8, -4, -8, -2],\n [-4, 9, -2, -1],\n [-8, -2, -11, 0],\n [-2, -1, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
836
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, -3, 2, -6],\n [0, 8, 0, 6],\n [0, 0, -9, -7],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
816
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-8, 1, -2, 9],\n [-6, -12, -11, 4],\n [-4, -11, -4, 10],\n [9, -5, 2, 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" } ]
759
MATH
[ { "content": "What is the determinant of the matrix:\n[[-1, -10, -4, 5],\n [-1, -6, 12, 8],\n [-11, 3, 10, -10],\n [-6, -6, -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" } ]
682
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, -4, 8, -12],\n [0, -8, 11, 6],\n [0, 0, 8, 4],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
24
MATH
[ { "content": "Determine the value of det(A) where A =\n[[7, 9, -6, 8],\n [-2, -4, -8, 0],\n [7, -3, 0, -4],\n [-11, -6, 12, -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": "What is the determinant of the matrix:\n[[6, -6, -1, 1],\n [10, 11, -1, -3],\n [-12, 1, 12, -5],\n [-11, -4, 3, -12]]? 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[[4, -11, -12, -2],\n [5, -6, -5, 5],\n [5, 7, -11, -9],\n [-6, 11, -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" } ]
198
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, -6, 2, 1],\n [-6, 11, -2, -4],\n [2, -2, 5, -7],\n [1, -4, -7, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
228
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 0, -7, 1],\n [0, 10, -11, 8],\n [0, 0, 9, -4],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
400
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, 1, -12, -1],\n [0, -8, 6, 2],\n [0, 0, -10, 6],\n [0, 0, 0, -3]]\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[[-2, -10, 6, 2],\n [-10, 11, -4, 4],\n [6, -4, -5, 0],\n [2, 4, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
350
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-3, -4, 5, -8],\n [-5, 10, -3, 1],\n [-10, 11, -4, 12],\n [4, -12, 11, 11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
355
MATH
[ { "content": "What is the determinant of the matrix:\n[[0, -4, 0, 1],\n [-4, -11, -4, -3],\n [0, -4, -11, -4],\n [1, -3, -4, 2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
367
MATH
[ { "content": "Compute |A| for the matrix A =\n[[9, -5, 7, -5],\n [0, -12, -5, -11],\n [0, 0, 3, -4],\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" } ]
380
MATH
[ { "content": "What is the determinant of the matrix:\n[[-4, 7, 9, -8],\n [0, -11, 5, -11],\n [-11, -1, -8, 7],\n [-8, 7, -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" } ]
460
MATH
[ { "content": "Compute |A| for the matrix A =\n[[3, 8, 0, -6],\n [8, -3, 3, -2],\n [0, 3, -9, -4],\n [-6, -2, -4, 12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
452
MATH
[ { "content": "Determine the value of det(A) where A =\n[[5, 12, 4, -8],\n [12, 4, 3, 0],\n [4, 3, 11, 10],\n [-8, 0, 10, 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" } ]
880
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, -1, 0, -4],\n [6, -9, -2, 11],\n [-9, -2, 6, -11],\n [10, -6, 4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
640
MATH
[ { "content": "What is the determinant of the matrix:\n[[-4, 4, -2, -4],\n [4, 1, -4, 1],\n [-2, -4, -10, -4],\n [-4, 1, -4, -6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
396
MATH
[ { "content": "What is the determinant of the matrix:\n[[-4, 11, 4, 12],\n [3, -2, -2, 10],\n [1, 7, -7, -12],\n [-9, 6, 1, 1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
689
MATH
[ { "content": "Compute |A| for the matrix A =\n[[11, 8, -1, 5],\n [-8, -6, 0, 0],\n [12, -9, -5, 5],\n [1, 0, 6, -10]]\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": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, 6, -2, 5],\n [-9, 8, 12, 5],\n [7, 11, 3, -5],\n [11, -1, -8, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
890
MATH
[ { "content": "Compute |A| for the matrix A =\n[[8, 9, 11, 7],\n [0, 4, -6, -11],\n [0, 0, 1, -9],\n [0, 0, 0, -2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
936
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, -2, 0, 4],\n [-2, 4, 2, -4],\n [0, 2, -4, -4],\n [4, -4, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
592
MATH
[ { "content": "What is the determinant of the matrix:\n[[7, -6, 9, 1],\n [0, 7, -4, 1],\n [0, 0, 11, 4],\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" } ]
532
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, -4, -4, -5],\n [6, -11, -3, -12],\n [-11, -3, -5, 8],\n [3, -5, -10, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
683
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, -6, -9, 6],\n [-4, 2, 9, 6],\n [3, 9, 2, -4],\n [0, -2, -10, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
685
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, 4, 10, 4],\n [0, -8, 4, 3],\n [0, 0, -5, -10],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
560
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, -4, 1, -9],\n [-11, 12, -6, -1],\n [4, 4, -10, -6],\n [9, -3, 7, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
162
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, 0, -2, 1],\n [2, 1, -6, -7],\n [9, -3, 7, -9],\n [6, -8, -10, 5]]\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[[2, 3, 8, -5],\n [-5, 9, -10, 11],\n [-9, -9, -9, -10],\n [-7, 2, -4, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
893
MATH
[ { "content": "What is the determinant of the matrix:\n[[1, 1, -6, -7],\n [-9, -8, -7, -4],\n [-7, -8, -3, -12],\n [-9, 0, 5, 2]]? 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": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, -2, 2, 6],\n [0, -5, -5, -10],\n [0, 0, -3, 6],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
240
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, -3, 12, 4],\n [0, 5, 1, 1],\n [0, 0, -9, 2],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
920
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, 12, 8, 0],\n [-12, -10, 9, 5],\n [6, 1, -2, -7],\n [10, 12, -5, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
675
MATH
[ { "content": "What is the determinant of the matrix:\n[[12, -8, 1, 0],\n [-8, 9, 2, -3],\n [1, 2, 10, -1],\n [0, -3, -1, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
375
MATH
[ { "content": "What is the determinant of the matrix:\n[[12, -8, 0, 2],\n [-8, 1, 9, 10],\n [0, 9, -6, 0],\n [2, 10, 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" } ]
168
MATH
[ { "content": "What is the determinant of the matrix:\n[[-5, -9, -10, -6],\n [-9, -10, -3, 2],\n [-10, -3, 1, 4],\n [-6, 2, 4, 1]]? 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