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[ { "content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-4, 0, 10, 10, -4, 8],\n [0, 12, 9, -2, 4, -14],\n [10, 9, -1, 4, 3, 8],\n [10, -2, 4, 7, -2, 1],\n [-4, 4, 3, -2, 13, -6],\n [8, -14, 8, 1, -6, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
94
MATH
[ { "content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[13, 2, -8, -8, 4, 10],\n [2, -1, -12, -7, 2, -7],\n [-8, -12, -4, -12, -4, -11],\n [-8, -7, -12, -6, -8, -2],\n [4, 2, -4, -8, -9, 4],\n [10, -7, -11, -2, 4, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
95
MATH
[ { "content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[4, -12, 6, -6, 10, 10],\n [0, -4, 1, -2, -2, 9],\n [0, 0, 9, 4, -5, 0],\n [0, 0, 0, -10, 8, 3],\n [0, 0, 0, 0, 13, -12],\n [0, 0, 0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
13
MATH
[ { "content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-11, -10, 5, 6, -8, -9],\n [0, -6, -10, -2, -12, 12],\n [0, 0, 4, 1, 7, -9],\n [0, 0, 0, -13, 8, -11],\n [0, 0, 0, 0, -12, 8],\n [0, 0, 0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
13
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[15, 5, 13, 3, 1, 8],\n [5, 3, 8, 4, 2, 4],\n [13, 8, -10, 1, 0, 0],\n [3, 4, 1, -12, 8, 9],\n [1, 2, 0, 8, 15, 2],\n [8, 4, 0, 9, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
28
MATH
[ { "content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[9, 12, 6, -3, -15, 1],\n [0, -12, 4, 0, -1, 11],\n [0, 0, -1, -2, 12, -5],\n [0, 0, 0, 0, -11, 9],\n [0, 0, 0, 0, -13, -3],\n [0, 0, 0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
13
MATH
[ { "content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-10, 2, 0, -4, 8, 6],\n [2, -6, 0, -6, 0, 6],\n [0, 0, -11, -4, -4, -4],\n [-4, -6, -4, -10, 6, -11],\n [8, 0, -4, 6, -13, -11],\n [6, 6, -4, -11, -11, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
26
MATH
[ { "content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[-2, 8, 2, 2, 2, 12],\n [8, 8, 2, -12, 2, 6],\n [2, 2, -6, 10, 3, 1],\n [2, -12, 10, 12, 2, 2],\n [2, 2, 3, 2, 15, -6],\n [12, 6, 1, 2, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
91
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-12, 2, 3, 6, -4, 4],\n [2, 9, -2, -8, 4, -3],\n [3, -2, -10, 10, -4, -4],\n [6, -8, 10, 8, 4, 5],\n [-4, 4, -4, 4, -4, 6],\n [4, -3, -4, 5, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
21
MATH
[ { "content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-11, -13, 7, 10, -11, 8],\n [0, 3, 3, 9, 5, -4],\n [0, 0, -7, -15, 2, 5],\n [0, 0, 0, 9, -9, 6],\n [0, 0, 0, 0, 13, 13],\n [0, 0, 0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
52
MATH
[ { "content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[6, -4, -6, -14, -2, 5],\n [-4, -14, -4, -3, 0, 0],\n [-6, -4, 0, 4, -3, -6],\n [-14, -3, 4, 3, 6, -11],\n [-2, 0, -3, 6, -8, -4],\n [5, 0, -6, -11, -4, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
32
MATH
[ { "content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[1, -10, -2, 1, 11, 12],\n [-10, -2, 4, 8, 4, 11],\n [-2, 4, -1, 10, 2, 0],\n [1, 8, 10, -7, 4, 1],\n [11, 4, 2, 4, -14, 2],\n [12, 11, 0, 1, 2, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
92
MATH
[ { "content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[-6, 4, -13, -10, -9, 4],\n [0, 9, 11, 2, -5, 3],\n [0, 0, -5, 8, -4, -6],\n [0, 0, 0, 12, -7, -12],\n [0, 0, 0, 0, -7, -1],\n [0, 0, 0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
45
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[12, 4, -10, -4, -14, -9],\n [0, -13, -3, -13, 11, 2],\n [0, 0, -10, -15, 12, -15],\n [0, 0, 0, 12, 0, -5],\n [0, 0, 0, 0, -2, 6],\n [0, 0, 0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
13
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[0, -5, 2, -7, 6, -4],\n [-5, 14, 4, -2, -13, 12],\n [2, 4, 15, -1, 8, 12],\n [-7, -2, -1, -15, 1, 11],\n [6, -13, 8, 1, 14, -9],\n [-4, 12, 12, 11, -9, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
37
MATH
[ { "content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[-10, 6, -8, 0, 12, -8],\n [6, -5, -4, 6, 2, 0],\n [-8, -4, 8, 0, 8, -14],\n [0, 6, 0, 10, 7, -1],\n [12, 2, 8, 7, -15, 4],\n [-8, 0, -14, -1, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
34
MATH
[ { "content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[2, 8, -3, 4, 10, 6],\n [8, 1, 0, -9, -3, 0],\n [-3, 0, -13, -14, -2, 2],\n [4, -9, -14, -13, -9, 8],\n [10, -3, -2, -9, -7, 6],\n [6, 0, 2, 8, 6, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
34
MATH
[ { "content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-13, -6, 8, 5, -1, 0],\n [-6, 15, 2, -11, 6, 6],\n [8, 2, 4, -4, -4, 4],\n [5, -11, -4, -13, -2, 4],\n [-1, 6, -4, -2, -10, -2],\n [0, 6, 4, 4, -2, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
23
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-2, 2, 4, -7, 7, -2],\n [2, -13, 4, 12, 9, -4],\n [4, 4, 1, 0, -5, 10],\n [-7, 12, 0, 7, 4, 2],\n [7, 9, -5, 4, -13, -4],\n [-2, -4, 10, 2, -4, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
26
MATH
[ { "content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-2, 12, 0, 6, 10, 9],\n [12, 12, -4, 6, 1, -2],\n [0, -4, 5, 3, -8, 3],\n [6, 6, 3, -15, 6, -2],\n [10, 1, -8, 6, -13, -10],\n [9, -2, 3, -2, -10, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
94
MATH
[ { "content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-12, 5, 0, 0, -1, 1],\n [5, 6, -4, 2, 15, 1],\n [0, -4, 13, 0, 3, -2],\n [0, 2, 0, -5, -6, -6],\n [-1, 15, 3, -6, 0, 4],\n [1, 1, -2, -6, 4, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
22
MATH
[ { "content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-7, 0, -4, -6, 0, 2],\n [0, 8, -12, -4, 2, 8],\n [-4, -12, -4, 0, -6, 6],\n [-6, -4, 0, 3, 8, 4],\n [0, 2, -6, 8, 3, -11],\n [2, 8, 6, 4, -11, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
20
MATH
[ { "content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[-9, 12, 12, -12, 6, -4],\n [0, -13, 6, -4, -14, 8],\n [0, 0, 7, -7, -15, -8],\n [0, 0, 0, 6, 9, 2],\n [0, 0, 0, 0, 10, 11],\n [0, 0, 0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
54
MATH
[ { "content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[13, -3, 1, -13, -8, -2],\n [0, 0, -3, 4, 8, 1],\n [0, 0, -10, 1, -2, 1],\n [0, 0, 0, 4, 12, -15],\n [0, 0, 0, 0, 1, 14],\n [0, 0, 0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
13
MATH
[ { "content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[8, -3, -4, -5, -2, 6],\n [-3, 3, 4, 3, 5, -5],\n [-4, 4, -5, -2, 0, -4],\n [-5, 3, -2, -3, -12, 2],\n [-2, 5, 0, -12, -8, 6],\n [6, -5, -4, 2, 6, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
26
MATH
[ { "content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-3, 1, -6, 7, 12, 0],\n [1, 9, 5, 0, -2, 3],\n [-6, 5, 7, -6, 0, 4],\n [7, 0, -6, -12, 2, -7],\n [12, -2, 0, 2, 3, -8],\n [0, 3, 4, -7, -8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
73
MATH
[ { "content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[10, 9, -3, 0, -2, -12],\n [9, 13, -5, -6, -12, -5],\n [-3, -5, -6, 4, 6, 2],\n [0, -6, 4, -9, 8, 0],\n [-2, -12, 6, 8, -14, 2],\n [-12, -5, 2, 0, 2, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
96
MATH
[ { "content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[1, -11, 10, 2, -4, 1],\n [-11, 7, 6, 4, 2, -9],\n [10, 6, 1, 12, 8, 7],\n [2, 4, 12, -10, 0, -2],\n [-4, 2, 8, 0, -13, 4],\n [1, -9, 7, -2, 4, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
24
MATH
[ { "content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[12, -4, -10, -12, -2, 10],\n [-4, -1, -4, 14, 10, -12],\n [-10, -4, 10, -2, -1, -4],\n [-12, 14, -2, 8, -9, -8],\n [-2, 10, -1, -9, -12, -4],\n [10, -12, -4, -8, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
37
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[13, -6, 6, 1, 14, 0],\n [-6, -1, 8, 8, 1, 2],\n [6, 8, -10, -2, -4, -3],\n [1, 8, -2, -4, -6, -2],\n [14, 1, -4, -6, 2, -12],\n [0, 2, -3, -2, -12, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
77
MATH
[ { "content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[-3, -8, 10, 0, -6, 9],\n [-8, 11, 4, 6, -6, -8],\n [10, 4, -1, 9, 10, -2],\n [0, 6, 9, -11, -8, 12],\n [-6, -6, 10, -8, -12, 0],\n [9, -8, -2, 12, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
98
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[-1, 14, 4, 1, -3, 0],\n [0, -12, -11, -11, -7, 1],\n [0, 0, -3, 6, 5, 11],\n [0, 0, 0, -6, -14, -3],\n [0, 0, 0, 0, -2, 15],\n [0, 0, 0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
36
MATH
[ { "content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[3, -14, 8, 4, -2, 7],\n [-14, -3, 6, -4, -7, -12],\n [8, 6, 1, -2, 8, -5],\n [4, -4, -2, 8, 1, 4],\n [-2, -7, 8, 1, 12, -4],\n [7, -12, -5, 4, -4, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
87
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[11, 5, -14, -5, 6, -3],\n [0, -4, 6, 5, 6, -5],\n [0, 0, -11, 1, 8, 4],\n [0, 0, 0, -4, -10, 1],\n [0, 0, 0, 0, -4, -4],\n [0, 0, 0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
46
MATH
[ { "content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-10, -3, -7, 13, 0, 0],\n [-3, 11, -1, 6, 0, 3],\n [-7, -1, 5, -2, -1, 0],\n [13, 6, -2, 15, 0, -6],\n [0, 0, -1, 0, 15, -3],\n [0, 3, 0, -6, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
78
MATH
[ { "content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[-15, -8, 3, 15, -10, -13],\n [0, -11, -3, -1, -2, 13],\n [0, 0, 0, 2, 6, 13],\n [0, 0, 0, 6, -6, -6],\n [0, 0, 0, 0, -14, -7],\n [0, 0, 0, 0, 0, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
60
MATH
[ { "content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[-1, -13, 3, 2, -8, 10],\n [0, -8, -9, 14, -9, -13],\n [0, 0, 9, -11, -15, -1],\n [0, 0, 0, -8, -11, 12],\n [0, 0, 0, 0, -13, -14],\n [0, 0, 0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
13
MATH
[ { "content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-2, -12, 14, 15, -10, -5],\n [0, -8, -13, -2, 12, -3],\n [0, 0, -3, 13, 3, 11],\n [0, 0, 0, -8, 1, 7],\n [0, 0, 0, 0, -10, 12],\n [0, 0, 0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
10
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[15, 10, -4, -4, -5, 4],\n [10, -2, 10, 4, 6, 6],\n [-4, 10, -9, 10, -3, -4],\n [-4, 4, 10, 5, 3, 6],\n [-5, 6, -3, 3, 9, 10],\n [4, 6, -4, 6, 10, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
93
MATH
[ { "content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-6, -12, -8, 6, 4, 4],\n [0, -2, 2, 12, -2, 4],\n [0, 0, -1, 6, 14, 15],\n [0, 0, 0, 7, -8, 2],\n [0, 0, 0, 0, -14, 2],\n [0, 0, 0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
14
MATH
[ { "content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[1, 6, 8, 2, 5, -2],\n [6, 10, 5, 1, -12, -2],\n [8, 5, 2, 0, -6, -11],\n [2, 1, 0, 13, 8, -8],\n [5, -12, -6, 8, -7, 6],\n [-2, -2, -11, -8, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
25
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[3, -3, 3, 1, -10, 0],\n [0, -4, 3, -11, 1, 10],\n [0, 0, 13, -15, 12, 11],\n [0, 0, 0, -6, -1, 7],\n [0, 0, 0, 0, -11, -15],\n [0, 0, 0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
38
MATH
[ { "content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[9, 14, -7, 5, 4, 3],\n [0, -4, -11, -6, 1, -11],\n [0, 0, -9, 12, -7, -13],\n [0, 0, 0, -2, -13, -4],\n [0, 0, 0, 0, -3, 2],\n [0, 0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
27
MATH
[ { "content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-7, -7, -10, -5, 6, 8],\n [0, -15, -12, -3, 7, -3],\n [0, 0, -7, 8, -8, -9],\n [0, 0, 0, 12, -10, -4],\n [0, 0, 0, 0, 6, 6],\n [0, 0, 0, 0, 0, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
60
MATH
[ { "content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-3, 7, -1, 4, -4, -1],\n [7, -4, -6, -4, -4, 3],\n [-1, -6, -10, 3, -12, 10],\n [4, -4, 3, -6, -6, 2],\n [-4, -4, -12, -6, -4, 8],\n [-1, 3, 10, 2, 8, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
70
MATH
[ { "content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[10, 10, 11, -8, -13, 6],\n [10, 12, 5, 5, -4, 1],\n [11, 5, -4, 5, -2, -2],\n [-8, 5, 5, 14, -1, -5],\n [-13, -4, -2, -1, 9, -3],\n [6, 1, -2, -5, -3, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
87
MATH
[ { "content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-4, 0, 0, -5, 5, -12],\n [0, -9, -12, -1, 3, -7],\n [0, 0, -15, 7, 9, 8],\n [0, 0, 0, 11, -12, -8],\n [0, 0, 0, 0, -14, -14],\n [0, 0, 0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
15
MATH
[ { "content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[10, -12, 11, -6, -6, 6],\n [-12, 8, 5, -4, 3, -4],\n [11, 5, -7, -2, 4, 1],\n [-6, -4, -2, 9, 6, -2],\n [-6, 3, 4, 6, -5, -2],\n [6, -4, 1, -2, -2, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
29
MATH
[ { "content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[12, 0, -3, -7, -2, 5],\n [0, -10, 12, 4, 10, -2],\n [-3, 12, -7, -6, 4, 4],\n [-7, 4, -6, 4, -6, 3],\n [-2, 10, 4, -6, 2, 0],\n [5, -2, 4, 3, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
25
MATH
[ { "content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[-2, -11, -10, -10, 14, 6],\n [0, 2, -2, -6, -2, -3],\n [0, 0, -13, 14, -10, 13],\n [0, 0, 0, -5, -4, -15],\n [0, 0, 0, 0, 2, -5],\n [0, 0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
24
MATH
[ { "content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-12, -2, 10, 3, 6, 3],\n [-2, 14, 6, -1, 4, -8],\n [10, 6, 3, 8, 9, -2],\n [3, -1, 8, -10, 0, -2],\n [6, 4, 9, 0, -14, -6],\n [3, -8, -2, -2, -6, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
98
MATH
[ { "content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[7, -8, -3, -6, -8, 14],\n [0, -1, 14, -15, -5, -9],\n [0, 0, 4, 8, 2, 6],\n [0, 0, 0, -7, -11, -6],\n [0, 0, 0, 0, -6, 15],\n [0, 0, 0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
33
MATH
[ { "content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-14, 7, -8, 0, 11, 6],\n [0, 11, 9, 13, -13, -4],\n [0, 0, -6, -12, -7, 6],\n [0, 0, 0, -14, 3, -15],\n [0, 0, 0, 0, -13, 4],\n [0, 0, 0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
14
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[-9, 11, 10, -2, 1, 2],\n [0, 4, 13, 4, 5, 11],\n [0, 0, -15, 2, -15, 10],\n [0, 0, 0, 4, 7, -6],\n [0, 0, 0, 0, -11, 10],\n [0, 0, 0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
46
MATH
[ { "content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-7, 8, -4, -10, -8, 6],\n [8, 5, -8, 3, 8, 0],\n [-4, -8, 12, -8, -4, 10],\n [-10, 3, -8, -11, 4, -5],\n [-8, 8, -4, 4, -1, -2],\n [6, 0, 10, -5, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
86
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[3, 4, -10, -5, 10, 4],\n [4, 11, -14, 12, 4, -6],\n [-10, -14, -13, 6, 1, 9],\n [-5, 12, 6, -12, -13, 9],\n [10, 4, 1, -13, -13, -3],\n [4, -6, 9, 9, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
34
MATH
[ { "content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[7, 6, -2, 3, 0, 0],\n [6, -7, 0, 2, 6, 1],\n [-2, 0, -11, 0, 0, -2],\n [3, 2, 0, 5, 6, 10],\n [0, 6, 0, 6, -12, 0],\n [0, 1, -2, 10, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
18
MATH
[ { "content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[-7, -11, -3, 7, 10, 2],\n [0, 14, -11, 9, 0, 11],\n [0, 0, 9, 14, 0, 11],\n [0, 0, 0, -9, 0, 8],\n [0, 0, 0, 0, -8, 1],\n [0, 0, 0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
14
MATH
[ { "content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[11, -10, 8, 2, -2, -6],\n [-10, -6, 5, 0, -6, -10],\n [8, 5, -1, 5, 6, 2],\n [2, 0, 5, -15, 4, 0],\n [-2, -6, 6, 4, 15, 10],\n [-6, -10, 2, 0, 10, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
24
MATH
[ { "content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-15, 6, 10, 7, -6, 7],\n [6, 9, -3, -4, 6, -10],\n [10, -3, -3, -12, -6, 7],\n [7, -4, -12, 1, 6, 0],\n [-6, 6, -6, 6, 7, -14],\n [7, -10, 7, 0, -14, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
99
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[2, -4, 8, -1, 4, -12],\n [-4, -2, 8, -12, 2, -11],\n [8, 8, -12, 8, -2, 5],\n [-1, -12, 8, -15, -5, -4],\n [4, 2, -2, -5, 11, 7],\n [-12, -11, 5, -4, 7, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
39
MATH
[ { "content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[3, 2, -7, 2, -2, -1],\n [2, 4, 12, -10, -2, 4],\n [-7, 12, 6, 0, 8, -10],\n [2, -10, 0, 8, 5, 0],\n [-2, -2, 8, 5, 3, -6],\n [-1, 4, -10, 0, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
23
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[-4, 14, 5, -5, -11, 11],\n [0, 1, -10, -15, -11, 9],\n [0, 0, -11, 6, 8, 11],\n [0, 0, 0, 0, -7, 3],\n [0, 0, 0, 0, 14, -1],\n [0, 0, 0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
36
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-9, -1, 7, -2, 7, 3],\n [0, 13, 8, 4, 13, 8],\n [0, 0, -6, -7, 9, -8],\n [0, 0, 0, -6, 1, -14],\n [0, 0, 0, 0, 14, -7],\n [0, 0, 0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
14
MATH
[ { "content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[11, -2, 4, -7, 0, -8],\n [-2, -14, 8, -3, 2, -6],\n [4, 8, -6, -10, 8, 7],\n [-7, -3, -10, 11, 3, -7],\n [0, 2, 8, 3, 6, 2],\n [-8, -6, 7, -7, 2, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
28
MATH
[ { "content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[14, 5, -14, 6, -13, -10],\n [0, 11, -6, -7, -15, 0],\n [0, 0, 11, -12, 11, 12],\n [0, 0, 0, -15, 3, 10],\n [0, 0, 0, 0, 11, 6],\n [0, 0, 0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
68
MATH
[ { "content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[-12, -14, 14, 9, -3, 12],\n [0, 1, -3, -12, -9, 1],\n [0, 0, 3, -15, -6, -12],\n [0, 0, 0, -6, -10, 0],\n [0, 0, 0, 0, 11, 6],\n [0, 0, 0, 0, 0, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
48
MATH
[ { "content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[9, 12, 6, 0, -4, -1],\n [12, -7, 6, 7, 5, 8],\n [6, 6, -5, 3, -4, -4],\n [0, 7, 3, -8, -2, -5],\n [-4, 5, -4, -2, -1, 5],\n [-1, 8, -4, -5, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
71
MATH
[ { "content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-14, 3, 4, 14, 5, -3],\n [3, 10, -8, -1, -1, 5],\n [4, -8, 7, -9, -6, 0],\n [14, -1, -9, 11, 4, -2],\n [5, -1, -6, 4, -10, -12],\n [-3, 5, 0, -2, -12, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
25
MATH
[ { "content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-2, -6, 1, -7, 13, -10],\n [0, 9, -9, 1, 12, 12],\n [0, 0, -11, -7, 2, 8],\n [0, 0, 0, 13, 10, -5],\n [0, 0, 0, 0, -8, -12],\n [0, 0, 0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
55
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[2, -2, 5, -4, 2, 12],\n [-2, -3, -3, 6, -12, 1],\n [5, -3, 8, -12, 1, 0],\n [-4, 6, -12, -2, -10, -2],\n [2, -12, 1, -10, 5, 6],\n [12, 1, 0, -2, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
84
MATH
[ { "content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[2, -9, -13, -3, -1, 4],\n [0, -13, -12, -11, -15, -12],\n [0, 0, 11, 8, -6, 7],\n [0, 0, 0, 15, 10, 4],\n [0, 0, 0, 0, -2, 7],\n [0, 0, 0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
49
MATH
[ { "content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[10, 2, -4, -4, 8, 2],\n [2, -7, -2, 2, 3, -12],\n [-4, -2, -7, 1, 2, 0],\n [-4, 2, 1, 7, 3, -8],\n [8, 3, 2, 3, -7, 6],\n [2, -12, 0, -8, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
72
MATH
[ { "content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-1, 0, 7, -3, 1, 7],\n [0, 5, -14, -11, -10, -4],\n [0, 0, 6, 6, -15, 14],\n [0, 0, 0, -6, 3, -2],\n [0, 0, 0, 0, 3, -12],\n [0, 0, 0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
6
MATH
[ { "content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[-9, 6, -3, -4, 4, 0],\n [6, -1, 14, 8, -4, -1],\n [-3, 14, -7, -7, -1, 0],\n [-4, 8, -7, -6, -3, -8],\n [4, -4, -1, -3, -14, 8],\n [0, -1, 0, -8, 8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
28
MATH
[ { "content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-1, -3, 0, 1, 5, 13],\n [0, -9, 8, 10, 1, -9],\n [0, 0, 10, 1, -13, -9],\n [0, 0, 0, 5, -15, 1],\n [0, 0, 0, 0, 11, 13],\n [0, 0, 0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
11
MATH
[ { "content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[12, 4, 4, 0, -1, -1],\n [4, 8, -11, 2, 1, 2],\n [4, -11, 3, -3, 0, 10],\n [0, 2, -3, 13, 1, 6],\n [-1, 1, 0, 1, -13, -6],\n [-1, 2, 10, 6, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
81
MATH
[ { "content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[3, -2, -1, -11, 10, -12],\n [-2, -1, 6, -6, 0, 2],\n [-1, 6, 9, -1, -4, 0],\n [-11, -6, -1, 6, 6, -2],\n [10, 0, -4, 6, -13, 7],\n [-12, 2, 0, -2, 7, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
77
MATH
[ { "content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[14, -1, -2, 12, 6, -8],\n [-1, 15, 4, -2, 1, -2],\n [-2, 4, 1, 3, 2, 6],\n [12, -2, 3, 8, -4, 7],\n [6, 1, 2, -4, 10, 0],\n [-8, -2, 6, 7, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
25
MATH
[ { "content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[4, 7, 0, -2, -2, -4],\n [7, 11, -10, 14, -9, 4],\n [0, -10, 13, -2, 3, 6],\n [-2, 14, -2, 5, 8, -8],\n [-2, -9, 3, 8, 14, -6],\n [-4, 4, 6, -8, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
31
MATH
[ { "content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[0, -6, -7, 10, 8, 0],\n [-6, 11, -9, 0, 8, -2],\n [-7, -9, -5, 0, 7, -6],\n [10, 0, 0, -4, 2, 0],\n [8, 8, 7, 2, 14, -12],\n [0, -2, -6, 0, -12, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
30
MATH
[ { "content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[13, -2, 10, -8, 11, -2],\n [-2, -2, -4, 9, -12, -12],\n [10, -4, -9, 6, 2, -6],\n [-8, 9, 6, -10, 2, 10],\n [11, -12, 2, 2, -15, 9],\n [-2, -12, -6, 10, 9, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
105
MATH
[ { "content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[13, 5, -13, -1, -11, 12],\n [0, -2, 2, 0, -10, 9],\n [0, 0, 11, 8, -8, 15],\n [0, 0, 0, -3, -10, 2],\n [0, 0, 0, 0, 6, 13],\n [0, 0, 0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
13
MATH
[ { "content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[13, 6, 12, 12, 4, -12],\n [6, 11, -8, 10, 6, 8],\n [12, -8, 1, -5, 2, -4],\n [12, 10, -5, 6, 0, 11],\n [4, 6, 2, 0, -13, 4],\n [-12, 8, -4, 11, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
98
MATH
[ { "content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[-12, -3, 1, -1, 10, -9],\n [-3, 0, -1, 0, 8, -4],\n [1, -1, -12, 0, 6, 0],\n [-1, 0, 0, -6, 8, 1],\n [10, 8, 6, 8, 7, 10],\n [-9, -4, 0, 1, 10, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
29
MATH
[ { "content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[15, 6, -10, 2, 6, -6],\n [6, -12, 8, 6, -6, 8],\n [-10, 8, -2, 1, 0, 14],\n [2, 6, 1, 6, -1, 8],\n [6, -6, 0, -1, -11, 0],\n [-6, 8, 14, 8, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
91
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-6, -4, 2, -6, 1, -4],\n [-4, -1, -4, 0, 0, 10],\n [2, -4, 1, 8, -2, -6],\n [-6, 0, 8, 0, -10, -3],\n [1, 0, -2, -10, -8, 9],\n [-4, 10, -6, -3, 9, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
23
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[10, 8, -4, 0, -6, 2],\n [8, -10, -11, -10, 5, 2],\n [-4, -11, -4, 2, 0, -2],\n [0, -10, 2, -8, 8, 7],\n [-6, 5, 0, 8, 0, -2],\n [2, 2, -2, 7, -2, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
27
MATH
[ { "content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-1, 8, 0, 11, 5, 7],\n [0, 15, -7, -13, 3, 4],\n [0, 0, 1, -1, 15, 7],\n [0, 0, 0, 15, 5, 14],\n [0, 0, 0, 0, 5, 7],\n [0, 0, 0, 0, 0, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
50
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[3, -3, -8, -5, -3, -7],\n [-3, 10, -3, -1, -2, 0],\n [-8, -3, -6, -4, -2, -10],\n [-5, -1, -4, 14, 8, 2],\n [-3, -2, -2, 8, 7, 3],\n [-7, 0, -10, 2, 3, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
24
MATH
[ { "content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[12, 4, -10, 14, 4, -11],\n [4, -3, 2, -2, 2, 0],\n [-10, 2, 2, -2, 14, 0],\n [14, -2, -2, 6, -8, 6],\n [4, 2, 14, -8, 14, -2],\n [-11, 0, 0, 6, -2, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
93
MATH
[ { "content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-4, -8, 10, 10, 2, 0],\n [-8, 7, 4, 6, -7, 12],\n [10, 4, 5, 8, -6, 0],\n [10, 6, 8, 0, 0, -3],\n [2, -7, -6, 0, -6, -2],\n [0, 12, 0, -3, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
78
MATH
[ { "content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-7, -3, 0, -2, 0, 1],\n [-3, -3, -5, -4, 13, -2],\n [0, -5, 3, 7, 0, 5],\n [-2, -4, 7, 0, 10, -10],\n [0, 13, 0, 10, -8, -6],\n [1, -2, 5, -10, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
74
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[-3, 8, 4, 11, -2, 2],\n [8, -12, 12, -2, -1, 0],\n [4, 12, -10, 14, -12, 8],\n [11, -2, 14, -13, 6, -10],\n [-2, -1, -12, 6, 6, 14],\n [2, 0, 8, -10, 14, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
107
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-10, -3, -12, 4, 1, 2],\n [-3, 1, 12, 14, 10, 8],\n [-12, 12, 4, 7, 2, -3],\n [4, 14, 7, 10, 0, -2],\n [1, 10, 2, 0, -3, 10],\n [2, 8, -3, -2, 10, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
30
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[1, 2, 0, -2, -13, 3],\n [2, 1, 2, 10, -4, -6],\n [0, 2, 7, -2, 2, -1],\n [-2, 10, -2, 11, 3, -4],\n [-13, -4, 2, 3, 13, 8],\n [3, -6, -1, -4, 8, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
24
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[14, -9, -3, 2, 13, -2],\n [0, 2, -3, -5, 5, 14],\n [0, 0, 7, 1, -8, 3],\n [0, 0, 0, 4, -6, -4],\n [0, 0, 0, 0, 14, -15],\n [0, 0, 0, 0, 0, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
15
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-4, -7, 2, -14, -2, 2],\n [-7, -4, -12, -4, -6, 11],\n [2, -12, -8, 2, 4, 0],\n [-14, -4, 2, -6, 14, 4],\n [-2, -6, 4, 14, 1, -12],\n [2, 11, 0, 4, -12, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
28
MATH
[ { "content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[8, -10, 6, 2, -10, -11],\n [0, 3, 6, -8, -7, 1],\n [0, 0, -5, 8, 1, 5],\n [0, 0, 0, -8, 3, -9],\n [0, 0, 0, 0, 3, 8],\n [0, 0, 0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
11
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[3, 0, -6, 4, 9, 0],\n [0, -12, 2, 4, 8, 1],\n [-6, 2, -12, 10, 12, -8],\n [4, 4, 10, -13, -8, 4],\n [9, 8, 12, -8, -6, -1],\n [0, 1, -8, 4, -1, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
79
MATH