messages
listlengths 1
1
| ground_truth
stringclasses 104
values | dataset
stringclasses 1
value |
|---|---|---|
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[-15, -13, 5, 10, 15, 11],\n [0, -15, -13, -13, -11, 3],\n [0, 0, -15, -12, 13, 13],\n [0, 0, 0, 1, -2, 2],\n [0, 0, 0, 0, -13, 7],\n [0, 0, 0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
70
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[-5, 15, 5, 10, -7, 10],\n [0, -10, 8, -5, -7, 13],\n [0, 0, 12, -13, -15, 4],\n [0, 0, 0, -2, 1, 6],\n [0, 0, 0, 0, -2, -4],\n [0, 0, 0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
35
|
MATH
|
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[7, 3, -10, -9, -15, -15],\n [0, -11, -10, 15, 0, 15],\n [0, 0, -2, -15, -3, 4],\n [0, 0, 0, -7, 15, -3],\n [0, 0, 0, 0, -14, 1],\n [0, 0, 0, 0, 0, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
15
|
MATH
|
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-14, -1, 2, -2, 10, -14],\n [-1, 12, 2, 6, 14, -2],\n [2, 2, 7, 2, 2, -6],\n [-2, 6, 2, -15, -6, 5],\n [10, 14, 2, -6, 4, -12],\n [-14, -2, -6, 5, -12, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
107
|
MATH
|
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[-14, 8, 5, -2, -9, 2],\n [8, 10, -5, -4, -6, 4],\n [5, -5, -3, 4, -4, 12],\n [-2, -4, 4, 14, 4, -2],\n [-9, -6, -4, 4, -7, -10],\n [2, 4, 12, -2, -10, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
94
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[0, -3, -6, 4, 2, -2],\n [-3, -15, -4, 4, -2, 3],\n [-6, -4, 0, 10, -2, -6],\n [4, 4, 10, -5, -10, -4],\n [2, -2, -2, -10, -11, -2],\n [-2, 3, -6, -4, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
67
|
MATH
|
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[4, -2, -2, 1, 5, -2],\n [-2, 12, -2, -11, -2, 12],\n [-2, -2, 7, -2, -6, 9],\n [1, -11, -2, 1, 13, -6],\n [5, -2, -6, 13, -3, -12],\n [-2, 12, 9, -6, -12, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
85
|
MATH
|
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-9, -15, 15, 7, 13, -4],\n [0, 8, -8, 9, -10, 12],\n [0, 0, 3, 4, 4, 8],\n [0, 0, 0, 0, 14, -12],\n [0, 0, 0, 0, 0, 11],\n [0, 0, 0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
26
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[-7, 1, 2, 9, 2, -8],\n [1, -3, -12, -6, -6, 12],\n [2, -12, -15, 4, -4, 1],\n [9, -6, 4, 0, 4, 6],\n [2, -6, -4, 4, 13, -10],\n [-8, 12, 1, 6, -10, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
89
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-8, -6, 1, -4, 7, 14],\n [-6, -1, 8, 6, 0, -4],\n [1, 8, 0, -3, -2, -6],\n [-4, 6, -3, 5, 13, 0],\n [7, 0, -2, 13, 0, -4],\n [14, -4, -6, 0, -4, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
23
|
MATH
|
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[9, -5, -3, 5, -5, -3],\n [-5, -13, -2, -1, 8, -4],\n [-3, -2, -4, -8, -10, 4],\n [5, -1, -8, 11, -7, -6],\n [-5, 8, -10, -7, -13, 2],\n [-3, -4, 4, -6, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
25
|
MATH
|
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-3, 11, -2, 0, 4, -7],\n [11, -3, 6, -3, -4, 9],\n [-2, 6, 6, -3, 9, -4],\n [0, -3, -3, 4, -4, 4],\n [4, -4, 9, -4, -5, -4],\n [-7, 9, -4, 4, -4, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
27
|
MATH
|
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[5, -3, 15, 13, -7, 11],\n [0, -9, 7, 8, 15, -11],\n [0, 0, 14, -7, -10, 9],\n [0, 0, 0, -14, -6, 0],\n [0, 0, 0, 0, -3, -1],\n [0, 0, 0, 0, 0, -12]]\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[[10, -4, 3, -1, 7, -8],\n [-4, -15, -2, 3, 0, 0],\n [3, -2, -13, -5, -9, -2],\n [-1, 3, -5, 2, -6, 5],\n [7, 0, -9, -6, -15, 8],\n [-8, 0, -2, 5, 8, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
82
|
MATH
|
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-12, -1, 2, -2, -2, -1],\n [-1, -3, 4, 4, -4, 0],\n [2, 4, -15, -6, -6, 6],\n [-2, 4, -6, -8, -3, -8],\n [-2, -4, -6, -3, -12, 10],\n [-1, 0, 6, -8, 10, -3]]\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[[-2, 4, 11, 0, 3, 0],\n [4, 15, -12, 10, 12, -8],\n [11, -12, -3, 8, -8, 2],\n [0, 10, 8, -15, -8, 6],\n [3, 12, -8, -8, -10, 2],\n [0, -8, 2, 6, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
31
|
MATH
|
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[12, -8, 6, -12, -5, -8],\n [0, 10, -14, 0, 15, -10],\n [0, 0, 10, 11, 3, 12],\n [0, 0, 0, 0, -4, -11],\n [0, 0, 0, 0, 3, 2],\n [0, 0, 0, 0, 0, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
48
|
MATH
|
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-14, -6, -15, 0, 4, 4],\n [-6, -12, -6, 8, 6, 2],\n [-15, -6, 13, -6, -1, 9],\n [0, 8, -6, 2, 0, -4],\n [4, 6, -1, 0, 7, -2],\n [4, 2, 9, -4, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
80
|
MATH
|
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[6, 7, 8, 2, -3, -6],\n [7, 14, 3, 8, 2, -3],\n [8, 3, -11, 0, -10, 2],\n [2, 8, 0, -9, -8, 0],\n [-3, 2, -10, -8, -10, -4],\n [-6, -3, 2, 0, -4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
80
|
MATH
|
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-9, -2, 10, 7, -6, -4],\n [-2, 13, 8, -6, 9, 2],\n [10, 8, -15, -10, 2, 1],\n [7, -6, -10, -13, 4, -1],\n [-6, 9, 2, 4, 7, 2],\n [-4, 2, 1, -1, 2, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
32
|
MATH
|
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-6, 6, 5, 0, 2, -10],\n [6, 12, 0, 13, -4, 4],\n [5, 0, 10, 6, 1, -2],\n [0, 13, 6, -15, 10, 2],\n [2, -4, 1, 10, -14, 0],\n [-10, 4, -2, 2, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
29
|
MATH
|
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[1, -14, -9, -9, -6, 6],\n [0, -13, 14, -4, -13, -5],\n [0, 0, 9, -12, 9, 0],\n [0, 0, 0, -12, 6, -10],\n [0, 0, 0, 0, -13, -11],\n [0, 0, 0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
55
|
MATH
|
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[14, -14, 5, 6, -10, -2],\n [-14, 8, 0, -4, 3, 6],\n [5, 0, -9, -5, -8, -5],\n [6, -4, -5, -9, -6, 2],\n [-10, 3, -8, -6, -14, -6],\n [-2, 6, -5, 2, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
30
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[-5, 10, 3, 4, -4, -4],\n [10, 8, -5, 0, -9, 12],\n [3, -5, 2, 2, -12, 8],\n [4, 0, 2, -8, -2, -4],\n [-4, -9, -12, -2, -14, 2],\n [-4, 12, 8, -4, 2, 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[[-12, 2, 10, -8, -5, 7],\n [2, 10, -1, 5, 6, -8],\n [10, -1, 6, -7, -4, 2],\n [-8, 5, -7, -11, 6, 0],\n [-5, 6, -4, 6, 7, 0],\n [7, -8, 2, 0, 0, -9]]\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[[13, -10, -7, -4, -1, 5],\n [0, -13, -6, -15, 3, 3],\n [0, 0, -3, 15, -4, -15],\n [0, 0, 0, 0, 9, 7],\n [0, 0, 0, 0, -5, 8],\n [0, 0, 0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
13
|
MATH
|
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-15, -1, -8, 8, 10, 2],\n [-1, -5, 4, 2, -2, -14],\n [-8, 4, 15, -3, 2, -2],\n [8, 2, -3, -13, -12, 4],\n [10, -2, 2, -12, -15, 0],\n [2, -14, -2, 4, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
97
|
MATH
|
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[8, 7, -5, -11, 2, 5],\n [7, -3, 10, 3, -6, 1],\n [-5, 10, 7, 0, 4, 10],\n [-11, 3, 0, 1, -2, -3],\n [2, -6, 4, -2, -2, -9],\n [5, 1, 10, -3, -9, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
75
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[-9, 10, -1, -1, 8, -10],\n [0, -10, 15, 0, -14, 15],\n [0, 0, 14, -5, 10, 14],\n [0, 0, 0, 8, 4, -9],\n [0, 0, 0, 0, 7, 13],\n [0, 0, 0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
58
|
MATH
|
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-11, -1, 8, 0, -4, 6],\n [-1, 11, 10, -3, 1, 14],\n [8, 10, -7, 6, 2, 4],\n [0, -3, 6, 15, -10, 0],\n [-4, 1, 2, -10, 4, 4],\n [6, 14, 4, 0, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
28
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-8, 13, 15, -7, 14, 6],\n [0, -4, -5, -14, 2, -7],\n [0, 0, -13, 0, 3, -12],\n [0, 0, 0, 4, 9, 14],\n [0, 0, 0, 0, 1, 10],\n [0, 0, 0, 0, 0, 0]]\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[[4, -8, -13, -3, 10, 2],\n [-8, 9, -8, -11, -2, 5],\n [-13, -8, -4, 10, 0, -8],\n [-3, -11, 10, 6, 0, 0],\n [10, -2, 0, 0, -13, 4],\n [2, 5, -8, 0, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
91
|
MATH
|
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[-14, -10, -1, 6, 4, 1],\n [-10, -10, 2, -8, 6, 2],\n [-1, 2, 13, 6, 6, 8],\n [6, -8, 6, 8, -5, -6],\n [4, 6, 6, -5, 1, -6],\n [1, 2, 8, -6, -6, 12]]\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[[-15, 0, -4, -2, 2, -3],\n [0, -8, 2, 12, -2, -2],\n [-4, 2, 9, 0, 2, 10],\n [-2, 12, 0, 3, -2, -10],\n [2, -2, 2, -2, 12, 2],\n [-3, -2, 10, -10, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
21
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[11, 8, 0, 9, 0, -8],\n [8, -9, 4, -7, 6, -1],\n [0, 4, -14, 4, -14, -1],\n [9, -7, 4, 15, 10, 1],\n [0, 6, -14, 10, -1, 0],\n [-8, -1, -1, 1, 0, 11]]\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[[1, 6, 4, 4, -11, -2],\n [6, -12, -5, 0, -2, 0],\n [4, -5, -6, 0, -8, 10],\n [4, 0, 0, 4, 11, 12],\n [-11, -2, -8, 11, 13, 0],\n [-2, 0, 10, 12, 0, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
95
|
MATH
|
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[-15, 1, -7, -2, 5, 1],\n [1, 9, -7, 2, -3, 0],\n [-7, -7, 3, 7, 2, -4],\n [-2, 2, 7, 2, -4, -2],\n [5, -3, 2, -4, 1, -6],\n [1, 0, -4, -2, -6, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
19
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[12, 3, 0, 6, 9, 0],\n [0, 7, 5, 5, -5, -9],\n [0, 0, 9, 15, 14, -3],\n [0, 0, 0, 13, -12, 3],\n [0, 0, 0, 0, -10, -11],\n [0, 0, 0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
13
|
MATH
|
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-12, 4, -2, 12, 10, 12],\n [4, 0, -6, 2, -4, 0],\n [-2, -6, -10, 14, 5, -10],\n [12, 2, 14, 11, 10, 11],\n [10, -4, 5, 10, 3, 1],\n [12, 0, -10, 11, 1, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
99
|
MATH
|
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[3, -3, -5, -2, 0, -14],\n [-3, -5, -8, 0, 7, -4],\n [-5, -8, 9, 14, 8, 2],\n [-2, 0, 14, -9, -4, 4],\n [0, 7, 8, -4, 13, 10],\n [-14, -4, 2, 4, 10, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
96
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[3, -4, 8, 8, -3, 0],\n [-4, -8, -3, 8, 2, 8],\n [8, -3, -1, 6, 0, -6],\n [8, 8, 6, -6, 4, 6],\n [-3, 2, 0, 4, 13, 12],\n [0, 8, -6, 6, 12, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
22
|
MATH
|
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[1, 2, 1, -6, 2, 10],\n [2, 6, 4, -12, 9, -8],\n [1, 4, 0, -2, -6, 1],\n [-6, -12, -2, -11, -1, -6],\n [2, 9, -6, -1, -15, 10],\n [10, -8, 1, -6, 10, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
87
|
MATH
|
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[8, 0, 0, 12, 0, -5],\n [0, 0, 2, 12, 0, 7],\n [0, 2, -4, 6, -10, 12],\n [12, 12, 6, -14, 0, -2],\n [0, 0, -10, 0, -13, 8],\n [-5, 7, 12, -2, 8, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
89
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[-10, 4, -1, 8, 5, -9],\n [0, 13, 13, 14, 5, 11],\n [0, 0, 14, -12, 6, 2],\n [0, 0, 0, 2, 8, 8],\n [0, 0, 0, 0, -1, -11],\n [0, 0, 0, 0, 0, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
55
|
MATH
|
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[-13, 9, 8, 10, 12, 8],\n [9, 2, 5, -2, -1, 0],\n [8, 5, -8, 3, -6, -8],\n [10, -2, 3, 8, 7, 3],\n [12, -1, -6, 7, 15, -4],\n [8, 0, -8, 3, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
29
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[-11, 5, 3, 0, -5, 4],\n [5, -2, -6, 3, 5, -8],\n [3, -6, -12, 0, 1, -4],\n [0, 3, 0, -7, -5, -6],\n [-5, 5, 1, -5, -9, 2],\n [4, -8, -4, -6, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
61
|
MATH
|
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[13, -4, 0, 11, 0, -4],\n [-4, 15, 8, -5, -5, -2],\n [0, 8, 8, 0, -4, 14],\n [11, -5, 0, -13, 3, -1],\n [0, -5, -4, 3, -3, -5],\n [-4, -2, 14, -1, -5, -11]]\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[[-4, -15, -4, 6, -10, 3],\n [0, 0, 15, 3, -13, 7],\n [0, 0, 2, 10, -3, 10],\n [0, 0, 0, 12, 7, -13],\n [0, 0, 0, 0, -4, 15],\n [0, 0, 0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
30
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[-8, -2, -7, -10, 8, 0],\n [-2, 5, -4, -2, 4, 3],\n [-7, -4, -9, -2, 14, 8],\n [-10, -2, -2, 5, -8, 0],\n [8, 4, 14, -8, -8, 8],\n [0, 3, 8, 0, 8, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
85
|
MATH
|
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[-5, 4, -2, -4, 2, -2],\n [4, 10, -2, -5, 4, -4],\n [-2, -2, -4, -5, -4, -4],\n [-4, -5, -5, 0, -4, 8],\n [2, 4, -4, -4, -10, -4],\n [-2, -4, -4, 8, -4, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
22
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[9, 9, 8, 9, 0, 4],\n [0, -10, -11, 5, -12, -14],\n [0, 0, -7, 12, 1, -2],\n [0, 0, 0, -15, 13, 4],\n [0, 0, 0, 0, 2, -13],\n [0, 0, 0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
54
|
MATH
|
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[8, -8, -4, 2, -3, -5],\n [-8, -3, 11, 0, 2, 0],\n [-4, 11, 15, 10, -2, -6],\n [2, 0, 10, -4, 6, -1],\n [-3, 2, -2, 6, 3, 7],\n [-5, 0, -6, -1, 7, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
26
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[-10, 4, 4, 8, 8, 2],\n [4, -11, 9, -2, -5, 2],\n [4, 9, 10, -6, -10, 6],\n [8, -2, -6, -11, 8, -6],\n [8, -5, -10, 8, -15, -2],\n [2, 2, 6, -6, -2, 11]]\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[[12, 2, 1, 12, 4, -6],\n [2, 0, 2, -12, -6, 4],\n [1, 2, 10, -4, -12, 2],\n [12, -12, -4, 3, 4, -1],\n [4, -6, -12, 4, 15, -1],\n [-6, 4, 2, -1, -1, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
79
|
MATH
|
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[12, 4, 1, 0, -10, 3],\n [4, 4, -2, -2, 7, 5],\n [1, -2, -7, 5, 4, 1],\n [0, -2, 5, -15, -8, 0],\n [-10, 7, 4, -8, 0, 8],\n [3, 5, 1, 0, 8, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
71
|
MATH
|
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[7, 3, -8, 4, 11, 0],\n [3, 10, 0, 7, -5, 2],\n [-8, 0, 7, 2, 3, -9],\n [4, 7, 2, -2, 13, 6],\n [11, -5, 3, 13, 11, -8],\n [0, 2, -9, 6, -8, -4]]\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, 6, 3, 0, -8, -8],\n [6, 13, 10, 4, 2, -13],\n [3, 10, -9, 6, 12, 0],\n [0, 4, 6, -7, 2, -2],\n [-8, 2, 12, 2, -11, 0],\n [-8, -13, 0, -2, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
88
|
MATH
|
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-12, 4, 0, -12, 8, 2],\n [4, 13, 1, 2, -4, 8],\n [0, 1, 8, -4, -8, -10],\n [-12, 2, -4, -4, -2, 6],\n [8, -4, -8, -2, 6, 7],\n [2, 8, -10, 6, 7, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
25
|
MATH
|
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[12, 4, 0, 9, -1, -3],\n [4, 2, -8, 5, -3, -8],\n [0, -8, -4, -6, 4, 0],\n [9, 5, -6, 4, 6, 0],\n [-1, -3, 4, 6, 7, 0],\n [-3, -8, 0, 0, 0, 0]]\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[[-8, -7, 11, -12, 5, 15],\n [0, -8, 9, -9, -1, 5],\n [0, 0, -5, -7, -11, 9],\n [0, 0, 0, 13, -2, -12],\n [0, 0, 0, 0, -15, 8],\n [0, 0, 0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
15
|
MATH
|
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[-8, -5, -6, -4, 0, 6],\n [-5, -2, 3, 0, 6, 4],\n [-6, 3, 13, -2, -6, 4],\n [-4, 0, -2, -2, 4, 0],\n [0, 6, -6, 4, -12, 8],\n [6, 4, 4, 0, 8, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
76
|
MATH
|
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-7, 5, 9, 8, 4, -5],\n [0, -9, 5, -6, -12, -11],\n [0, 0, 15, -7, 12, 0],\n [0, 0, 0, -12, 15, -14],\n [0, 0, 0, 0, -10, -5],\n [0, 0, 0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
57
|
MATH
|
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[12, 10, 2, 3, -13, -7],\n [0, 15, 1, 1, 15, 7],\n [0, 0, -7, -7, -11, -1],\n [0, 0, 0, 12, -13, -10],\n [0, 0, 0, 0, 11, -3],\n [0, 0, 0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
58
|
MATH
|
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[6, 0, -8, 4, 8, 4],\n [0, 10, 8, 12, 0, 3],\n [-8, 8, 6, -4, 8, -4],\n [4, 12, -4, 4, -11, -4],\n [8, 0, 8, -11, -14, 0],\n [4, 3, -4, -4, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
25
|
MATH
|
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[10, 12, 0, 6, 0, -5],\n [12, -15, 8, 2, 9, 0],\n [0, 8, 2, 8, 6, -8],\n [6, 2, 8, 10, -8, -5],\n [0, 9, 6, -8, 6, 0],\n [-5, 0, -8, -5, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
91
|
MATH
|
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-13, 3, -6, 11, -1, -5],\n [0, 10, 11, 8, -3, -11],\n [0, 0, -7, 9, 1, -14],\n [0, 0, 0, -9, -15, 12],\n [0, 0, 0, 0, -4, 3],\n [0, 0, 0, 0, 0, -14]]\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[[9, 13, -12, 4, 7, 10],\n [0, -6, -3, -14, -13, 3],\n [0, 0, 11, 5, 4, 3],\n [0, 0, 0, -13, -10, 13],\n [0, 0, 0, 0, -2, 3],\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 sum of absolute values of all eigenvalues:\n[[-14, -10, -10, 1, 6, 2],\n [-10, 3, 10, 0, 8, -3],\n [-10, 10, 4, -2, -8, -10],\n [1, 0, -2, 1, 6, -6],\n [6, 8, -8, 6, 6, 2],\n [2, -3, -10, -6, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
89
|
MATH
|
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-8, -10, -4, -1, -2, 6],\n [-10, 6, -4, 2, -4, -2],\n [-4, -4, 4, -5, -8, 8],\n [-1, 2, -5, 6, -10, 2],\n [-2, -4, -8, -10, -3, 2],\n [6, -2, 8, 2, 2, -11]]\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, 0, -2, -2, 12, -2],\n [0, -13, -5, -4, -6, -3],\n [-2, -5, 13, 6, -13, 4],\n [-2, -4, 6, 8, 10, -6],\n [12, -6, -13, 10, -4, 0],\n [-2, -3, 4, -6, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
27
|
MATH
|
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[8, 1, 2, -6, 2, 7],\n [1, -6, -5, 0, -5, -6],\n [2, -5, 12, -4, 12, 2],\n [-6, 0, -4, -1, 6, -4],\n [2, -5, 12, 6, -14, 0],\n [7, -6, 2, -4, 0, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
22
|
MATH
|
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-11, -13, 9, -1, 3, -14],\n [0, -11, 6, 1, -2, 12],\n [0, 0, -6, -13, -12, -10],\n [0, 0, 0, 6, 0, -9],\n [0, 0, 0, 0, 12, 15],\n [0, 0, 0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
12
|
MATH
|
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-15, -11, -3, 5, -2, -7],\n [0, -1, 5, 15, -9, 11],\n [0, 0, -4, 7, -10, 5],\n [0, 0, 0, -7, -2, -8],\n [0, 0, 0, 0, 14, 4],\n [0, 0, 0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
44
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[-1, 4, 4, 6, 2, -12],\n [4, 5, -12, -2, 1, -2],\n [4, -12, 10, 4, 8, -4],\n [6, -2, 4, -1, 2, -6],\n [2, 1, 8, 2, -4, -1],\n [-12, -2, -4, -6, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
71
|
MATH
|
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-8, 0, -2, 1, -2, 1],\n [0, -8, -7, -2, -6, 2],\n [-2, -7, -9, -2, -6, 2],\n [1, -2, -2, -4, 2, -2],\n [-2, -6, -6, 2, -13, -4],\n [1, 2, 2, -2, -4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
23
|
MATH
|
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[-8, 1, 6, 2, -4, -4],\n [1, -3, 8, -4, 6, -6],\n [6, 8, -4, 12, 2, -6],\n [2, -4, 12, -3, 2, -4],\n [-4, 6, 2, 2, 5, -6],\n [-4, -6, -6, -4, -6, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
25
|
MATH
|
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[13, 6, -10, -6, -3, -6],\n [6, -6, -4, 4, 8, -1],\n [-10, -4, 1, 7, -7, 10],\n [-6, 4, 7, -4, 0, -6],\n [-3, 8, -7, 0, 15, 12],\n [-6, -1, 10, -6, 12, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
29
|
MATH
|
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[10, -6, 5, 10, 2, -2],\n [-6, -2, 9, 6, -6, -10],\n [5, 9, 13, 2, 6, -7],\n [10, 6, 2, -1, 6, 2],\n [2, -6, 6, 6, -5, 13],\n [-2, -10, -7, 2, 13, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
89
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[-2, -7, 2, -9, 12, 0],\n [-7, 14, -6, 4, 2, 2],\n [2, -6, -10, -8, 2, -4],\n [-9, 4, -8, 14, -12, 4],\n [12, 2, 2, -12, 4, -11],\n [0, 2, -4, 4, -11, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
88
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[5, 7, -4, 9, -14, -3],\n [0, 11, -12, 4, 2, 3],\n [0, 0, -2, 14, 13, -8],\n [0, 0, 0, 10, 2, -14],\n [0, 0, 0, 0, -10, -6],\n [0, 0, 0, 0, 0, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
51
|
MATH
|
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[-4, 5, 3, 0, -4, -5],\n [5, 15, 0, -10, 2, 8],\n [3, 0, -5, 5, 4, -2],\n [0, -10, 5, 7, 1, 7],\n [-4, 2, 4, 1, -9, 0],\n [-5, 8, -2, 7, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
23
|
MATH
|
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-8, -11, 0, 0, 2, -1],\n [-11, -4, -2, -4, 11, 8],\n [0, -2, 6, 6, -2, 2],\n [0, -4, 6, -11, 0, -8],\n [2, 11, -2, 0, 0, 2],\n [-1, 8, 2, -8, 2, -10]]\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[[-11, 1, -6, -4, -6, 6],\n [1, 2, 4, 8, 6, 6],\n [-6, 4, 11, 1, -2, -1],\n [-4, 8, 1, 13, -4, 9],\n [-6, 6, -2, -4, 6, -3],\n [6, 6, -1, 9, -3, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
22
|
MATH
|
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[6, 5, 2, 6, -2, -1],\n [5, -12, 12, 3, 6, -4],\n [2, 12, -3, -6, -4, -2],\n [6, 3, -6, -5, 9, -10],\n [-2, 6, -4, 9, -4, 8],\n [-1, -4, -2, -10, 8, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
76
|
MATH
|
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[13, -8, 2, 4, -5, 4],\n [-8, 5, 4, 5, 1, 2],\n [2, 4, 10, -5, 1, -6],\n [4, 5, -5, 9, 0, -4],\n [-5, 1, 1, 0, 9, -6],\n [4, 2, -6, -4, -6, -10]]\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[[8, -2, 1, 9, 3, -15],\n [0, -3, -2, 11, -10, 11],\n [0, 0, 14, -2, -13, 7],\n [0, 0, 0, 3, 12, 7],\n [0, 0, 0, 0, 11, 9],\n [0, 0, 0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
48
|
MATH
|
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[0, 12, -8, 4, -2, 3],\n [12, 6, 0, -5, 9, -2],\n [-8, 0, 2, -2, 6, -6],\n [4, -5, -2, -6, -6, 10],\n [-2, 9, 6, -6, -14, 5],\n [3, -2, -6, 10, 5, 5]]\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[[14, 12, -12, 10, -14, -8],\n [0, 0, 7, -5, 2, 6],\n [0, 0, 7, -1, 1, 5],\n [0, 0, 0, 14, -2, 7],\n [0, 0, 0, 0, 8, 15],\n [0, 0, 0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
53
|
MATH
|
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-14, 0, -7, -9, -8, 6],\n [0, 15, -10, 0, 10, 0],\n [-7, -10, 6, 0, 2, -12],\n [-9, 0, 0, 7, 3, 7],\n [-8, 10, 2, 3, -10, 4],\n [6, 0, -12, 7, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
100
|
MATH
|
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[-11, 6, 2, 8, -2, 14],\n [6, 5, 1, 8, -5, -4],\n [2, 1, 8, 2, -8, -2],\n [8, 8, 2, 9, 10, 0],\n [-2, -5, -8, 10, -10, 10],\n [14, -4, -2, 0, 10, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
87
|
MATH
|
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[0, -12, 5, 0, -4, -8],\n [-12, -11, 11, -9, 8, -4],\n [5, 11, -4, 1, 5, 0],\n [0, -9, 1, 0, 0, 14],\n [-4, 8, 5, 0, 7, 5],\n [-8, -4, 0, 14, 5, 1]]\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, -4, -6, -2, -9, 4],\n [-4, 0, 6, 4, 2, 9],\n [-6, 6, 1, -4, 0, 7],\n [-2, 4, -4, -6, 2, 2],\n [-9, 2, 0, 2, 2, 6],\n [4, 9, 7, 2, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
22
|
MATH
|
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[10, 1, -9, -2, -6, 0],\n [1, -10, -12, -7, 2, 6],\n [-9, -12, 13, -9, -8, -10],\n [-2, -7, -9, -14, -5, 6],\n [-6, 2, -8, -5, -5, 7],\n [0, 6, -10, 6, 7, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
32
|
MATH
|
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[-11, -14, -7, -10, 2, -2],\n [0, -2, -8, 1, 12, -13],\n [0, 0, 1, 11, -5, -8],\n [0, 0, 0, -12, -9, -2],\n [0, 0, 0, 0, -5, 1],\n [0, 0, 0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
12
|
MATH
|
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[3, -8, -4, 0, 4, -10],\n [-8, -7, 12, -5, 2, 11],\n [-4, 12, -14, -9, 1, 8],\n [0, -5, -9, -7, -8, 0],\n [4, 2, 1, -8, 15, -3],\n [-10, 11, 8, 0, -3, 11]]\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[[8, -4, 14, 4, 0, -13],\n [0, -15, -6, 15, -1, -9],\n [0, 0, 8, 0, -2, -13],\n [0, 0, 0, 2, -13, 14],\n [0, 0, 0, 0, 6, -11],\n [0, 0, 0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
15
|
MATH
|
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-5, -5, -8, -2, -9, -2],\n [-5, -8, -4, 2, -7, 0],\n [-8, -4, -12, -10, -4, -2],\n [-2, 2, -10, 3, 3, 0],\n [-9, -7, -4, 3, -7, 10],\n [-2, 0, -2, 0, 10, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
70
|
MATH
|
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[0, -13, -6, 8, -5, -8],\n [0, 4, -5, 12, 11, 5],\n [0, 0, 2, -3, 6, -13],\n [0, 0, 0, 5, -2, 2],\n [0, 0, 0, 0, -11, 5],\n [0, 0, 0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
12
|
MATH
|
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[7, 15, -1, 12, 13, -1],\n [0, 3, 10, 4, -10, 3],\n [0, 0, -8, -10, 4, 7],\n [0, 0, 0, -13, -6, -1],\n [0, 0, 0, 0, -5, 0],\n [0, 0, 0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
46
|
MATH
|
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-8, -6, -4, 8, 7, 10],\n [-6, -11, 8, 3, -2, -7],\n [-4, 8, 1, -6, -6, -11],\n [8, 3, -6, -10, -8, -2],\n [7, -2, -6, -8, -7, -2],\n [10, -7, -11, -2, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
30
|
MATH
|
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