messages
listlengths 1
1
| ground_truth
stringclasses 104
values | dataset
stringclasses 1
value |
|---|---|---|
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-9, 4, 13, -1, -5, -8],\n [0, 5, -9, 10, 3, 7],\n [0, 0, 8, 5, -12, -8],\n [0, 0, 0, 5, -14, 8],\n [0, 0, 0, 0, 12, 5],\n [0, 0, 0, 0, 0, -4]]\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[[9, 1, 11, 11, 15, -6],\n [0, 12, 0, -1, 14, 14],\n [0, 0, 3, -4, 7, 4],\n [0, 0, 0, 3, -9, 5],\n [0, 0, 0, 0, 9, 12],\n [0, 0, 0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
41
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-14, 0, 6, 6, 12, -8],\n [0, 13, -10, -6, 1, 6],\n [6, -10, 2, -1, -5, -13],\n [6, -6, -1, -6, -1, 2],\n [12, 1, -5, -1, -4, 0],\n [-8, 6, -13, 2, 0, 0]]\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[[-1, -8, -2, 7, 12, 9],\n [0, -8, 5, 0, -3, 2],\n [0, 0, 8, 10, 9, 12],\n [0, 0, 0, -7, 13, -1],\n [0, 0, 0, 0, -7, 8],\n [0, 0, 0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
8
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[3, 6, 2, -14, -12, -14],\n [6, -11, -8, -4, -2, -11],\n [2, -8, -7, 0, -4, -14],\n [-14, -4, 0, 7, 3, -2],\n [-12, -2, -4, 3, 6, 5],\n [-14, -11, -14, -2, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
33
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-13, -8, 0, 0, -2, 14],\n [-8, -9, 2, -3, 3, -6],\n [0, 2, 12, 0, -3, 6],\n [0, -3, 0, 13, -8, 2],\n [-2, 3, -3, -8, -1, 3],\n [14, -6, 6, 2, 3, 3]]\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[[6, 12, -14, -6, -3, 14],\n [0, 5, -10, 12, 12, -4],\n [0, 0, 14, 14, -5, 10],\n [0, 0, 0, -9, 14, -15],\n [0, 0, 0, 0, 9, 4],\n [0, 0, 0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
14
|
MATH
|
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[11, -6, 11, 0, -14, 7],\n [-6, -4, 0, 2, 6, 4],\n [11, 0, 4, -2, 2, -6],\n [0, 2, -2, 14, -4, -14],\n [-14, 6, 2, -4, 8, 6],\n [7, 4, -6, -14, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
90
|
MATH
|
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[7, -12, -14, 0, -4, 0],\n [-12, 5, 2, 0, -2, 0],\n [-14, 2, -5, 8, 3, 6],\n [0, 0, 8, -11, 10, -2],\n [-4, -2, 3, 10, 0, -5],\n [0, 0, 6, -2, -5, 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[[13, -5, -2, 7, 10, -12],\n [-5, 10, -4, 4, 2, -2],\n [-2, -4, -7, -15, 0, 2],\n [7, 4, -15, -5, 14, 4],\n [10, 2, 0, 14, 14, 2],\n [-12, -2, 2, 4, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
95
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[9, 2, 10, 0, -14, -14],\n [2, 14, -6, -12, -2, 0],\n [10, -6, -7, -4, 4, -4],\n [0, -12, -4, 8, 0, 6],\n [-14, -2, 4, 0, 1, 3],\n [-14, 0, -4, 6, 3, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
100
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[0, 8, 4, -14, 0, 4],\n [8, -2, 8, -8, -2, -1],\n [4, 8, -7, -4, -14, -4],\n [-14, -8, -4, 0, 2, 7],\n [0, -2, -14, 2, -15, 4],\n [4, -1, -4, 7, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
87
|
MATH
|
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-2, 10, 2, 1, -1, 0],\n [10, -8, -2, 12, -6, 5],\n [2, -2, 12, 0, -10, -10],\n [1, 12, 0, 3, 0, -13],\n [-1, -6, -10, 0, 14, 12],\n [0, 5, -10, -13, 12, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
92
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[-11, 12, 13, 5, -5, 6],\n [12, -13, 8, -10, 1, 0],\n [13, 8, 7, 0, -2, 8],\n [5, -10, 0, 6, 6, -1],\n [-5, 1, -2, 6, -1, 0],\n [6, 0, 8, -1, 0, -14]]\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[[10, 4, 1, -2, -2, -4],\n [4, 0, -11, 12, -10, 5],\n [1, -11, 2, 0, 0, 2],\n [-2, 12, 0, 9, -7, -2],\n [-2, -10, 0, -7, 0, 5],\n [-4, 5, 2, -2, 5, -14]]\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[[-14, 7, 15, 6, 3, 9],\n [0, 15, 14, 13, 6, 10],\n [0, 0, 1, 4, -6, -10],\n [0, 0, 0, 12, -11, -15],\n [0, 0, 0, 0, -4, -11],\n [0, 0, 0, 0, 0, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
60
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-1, -13, 7, -8, 4, 0],\n [0, 2, 12, -6, 14, 3],\n [0, 0, 15, 3, 12, 10],\n [0, 0, 0, 10, 5, 14],\n [0, 0, 0, 0, 5, -15],\n [0, 0, 0, 0, 0, 14]]\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[[6, 0, 9, -8, -3, 5],\n [0, 0, 13, -9, 15, -11],\n [0, 0, 7, -13, -4, 10],\n [0, 0, 0, 6, 9, 13],\n [0, 0, 0, 0, 1, 14],\n [0, 0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
7
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[10, -2, -3, 10, 0, -6],\n [-2, 14, 10, -8, -2, 8],\n [-3, 10, -11, -1, -8, -5],\n [10, -8, -1, 3, -1, -7],\n [0, -2, -8, -1, 0, 10],\n [-6, 8, -5, -7, 10, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
31
|
MATH
|
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[4, -4, -4, -2, -8, 10],\n [-4, -15, 0, 0, -10, -5],\n [-4, 0, -15, -1, 2, 2],\n [-2, 0, -1, -3, 0, 4],\n [-8, -10, 2, 0, 2, 0],\n [10, -5, 2, 4, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
75
|
MATH
|
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-6, 10, 14, -14, 3, -7],\n [0, -12, 10, 5, 2, -3],\n [0, 0, 8, -12, 9, 5],\n [0, 0, 0, -6, -11, -7],\n [0, 0, 0, 0, 0, -12],\n [0, 0, 0, 0, 0, 14]]\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[[-11, 2, 8, 9, -5, 2],\n [2, -13, -2, 8, 2, 8],\n [8, -2, 0, 5, 1, 0],\n [9, 8, 5, -12, -6, 8],\n [-5, 2, 1, -6, -9, 11],\n [2, 8, 0, 8, 11, -1]]\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[[0, 5, -11, -13, -4, 9],\n [0, 11, 5, -12, 5, 7],\n [0, 0, -9, -3, 5, -6],\n [0, 0, 0, 15, 10, -11],\n [0, 0, 0, 0, -5, 2],\n [0, 0, 0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
44
|
MATH
|
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[1, 13, -10, -9, -2, -3],\n [0, -6, -7, 2, 11, 10],\n [0, 0, 13, -11, -10, 3],\n [0, 0, 0, -15, 6, 4],\n [0, 0, 0, 0, -3, -12],\n [0, 0, 0, 0, 0, 13]]\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[[-4, 4, -4, 2, -10, 11],\n [4, -9, 13, 0, -3, -1],\n [-4, 13, 14, 12, 8, 10],\n [2, 0, 12, -7, 2, -4],\n [-10, -3, 8, 2, 9, 0],\n [11, -1, 10, -4, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
94
|
MATH
|
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[5, 2, 2, 0, -2, 2],\n [2, -1, 8, 4, 2, -4],\n [2, 8, -11, -5, 1, 2],\n [0, 4, -5, -1, -11, 4],\n [-2, 2, 1, -11, 5, 8],\n [2, -4, 2, 4, 8, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
22
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-4, 1, -6, 2, -2, 0],\n [1, 12, 8, 2, 12, 4],\n [-6, 8, -8, 0, 6, 7],\n [2, 2, 0, -7, -10, 6],\n [-2, 12, 6, -10, -15, 9],\n [0, 4, 7, 6, 9, -3]]\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[[-2, -12, 14, -1, 2, 4],\n [-12, -1, 6, -14, -6, 10],\n [14, 6, 11, 2, -3, 9],\n [-1, -14, 2, -15, 6, 0],\n [2, -6, -3, 6, 15, 3],\n [4, 10, 9, 0, 3, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
115
|
MATH
|
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-14, -4, 1, 2, -7, 4],\n [-4, 7, -10, 8, 3, -7],\n [1, -10, -10, -12, 2, 2],\n [2, 8, -12, -6, -6, -4],\n [-7, 3, 2, -6, -2, 0],\n [4, -7, 2, -4, 0, -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[[1, -8, -14, 4, 8, -10],\n [-8, 10, 10, -12, 3, 6],\n [-14, 10, 2, 5, 0, 2],\n [4, -12, 5, 14, 5, -2],\n [8, 3, 0, 5, 7, -3],\n [-10, 6, 2, -2, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
88
|
MATH
|
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-9, -10, 12, -14, -10, 2],\n [0, 2, 14, -1, 11, 3],\n [0, 0, 4, 9, -10, -15],\n [0, 0, 0, 14, 7, -6],\n [0, 0, 0, 0, -12, -6],\n [0, 0, 0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
45
|
MATH
|
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[8, -7, -6, 2, -2, -2],\n [-7, 14, -3, -5, -6, 4],\n [-6, -3, 9, 6, 8, 1],\n [2, -5, 6, 0, 0, 0],\n [-2, -6, 8, 0, -13, -2],\n [-2, 4, 1, 0, -2, 3]]\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[[3, 5, -11, 2, 12, -6],\n [0, 6, 5, -10, -15, -11],\n [0, 0, 10, -2, -14, 1],\n [0, 0, 0, 11, -7, 10],\n [0, 0, 0, 0, -1, 8],\n [0, 0, 0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
32
|
MATH
|
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[10, -12, -15, -8, 1, -13],\n [0, 4, -1, -1, 15, 8],\n [0, 0, 10, 12, 7, -2],\n [0, 0, 0, 10, -2, 11],\n [0, 0, 0, 0, -1, 7],\n [0, 0, 0, 0, 0, 2]]\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, -2, -6, 6, -4, -2],\n [-2, -11, 2, -2, -11, 4],\n [-6, 2, 6, 4, 4, 1],\n [6, -2, 4, 4, 3, -13],\n [-4, -11, 4, 3, 2, -1],\n [-2, 4, 1, -13, -1, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
20
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-8, -5, 2, -6, 0, 4],\n [-5, -10, 8, 8, -7, 12],\n [2, 8, -3, -2, -12, 12],\n [-6, 8, -2, 5, 2, -1],\n [0, -7, -12, 2, -5, 10],\n [4, 12, 12, -1, 10, -7]]\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[[7, -12, 8, 8, 0, -4],\n [-12, 8, 5, 2, -14, 0],\n [8, 5, -12, 4, -6, 1],\n [8, 2, 4, -10, -1, 2],\n [0, -14, -6, -1, -8, 0],\n [-4, 0, 1, 2, 0, 10]]\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[[6, -12, 3, 4, -15, 4],\n [0, -4, -1, -15, 10, -2],\n [0, 0, 14, -5, 15, -12],\n [0, 0, 0, -15, -10, 2],\n [0, 0, 0, 0, -6, -4],\n [0, 0, 0, 0, 0, -15]]\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[[15, -6, 4, 2, -10, 0],\n [-6, 8, -4, 2, -8, 13],\n [4, -4, -11, 10, 0, 4],\n [2, 2, 10, 8, -9, -8],\n [-10, -8, 0, -9, -15, -6],\n [0, 13, 4, -8, -6, -7]]\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[[-11, -2, 12, 14, -13, 5],\n [0, -11, 3, 11, -2, 10],\n [0, 0, 9, -3, -6, 9],\n [0, 0, 0, -9, -8, -2],\n [0, 0, 0, 0, 7, 15],\n [0, 0, 0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
11
|
MATH
|
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[7, -14, -2, 5, -8, -8],\n [0, -9, 3, -10, -10, -13],\n [0, 0, -8, -6, 4, -1],\n [0, 0, 0, 4, 14, -9],\n [0, 0, 0, 0, 9, -15],\n [0, 0, 0, 0, 0, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
51
|
MATH
|
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[-12, 0, -8, -4, -12, 7],\n [0, -15, -3, 2, -4, 9],\n [-8, -3, -3, 0, 0, -2],\n [-4, 2, 0, -11, 0, -6],\n [-12, -4, 0, 0, 11, 12],\n [7, 9, -2, -6, 12, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
91
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[11, -10, 7, -6, 3, -3],\n [-10, -10, -6, 3, 10, -6],\n [7, -6, -5, -1, 2, -7],\n [-6, 3, -1, 9, -10, 4],\n [3, 10, 2, -10, -4, -12],\n [-3, -6, -7, 4, -12, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
91
|
MATH
|
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[15, -6, 1, 12, 15, 10],\n [0, 6, 3, 13, -2, -8],\n [0, 0, -5, 7, -15, -2],\n [0, 0, 0, -2, -12, 6],\n [0, 0, 0, 0, 6, 7],\n [0, 0, 0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
41
|
MATH
|
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[5, -7, -6, 4, 9, 5],\n [0, -7, -13, 15, 4, 9],\n [0, 0, -10, -14, -9, 2],\n [0, 0, 0, 1, -5, 11],\n [0, 0, 0, 0, 8, 9],\n [0, 0, 0, 0, 0, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
15
|
MATH
|
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[1, 13, 15, -5, 6, 10],\n [0, 2, 5, 1, -9, 1],\n [0, 0, 1, 4, 6, 6],\n [0, 0, 0, -8, 1, -9],\n [0, 0, 0, 0, 3, 11],\n [0, 0, 0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
8
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-3, 8, 0, -5, 2, 3],\n [8, -15, 2, 3, 3, 0],\n [0, 2, 12, 8, -4, 0],\n [-5, 3, 8, -12, -14, 2],\n [2, 3, -4, -14, -6, -10],\n [3, 0, 0, 2, -10, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
27
|
MATH
|
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[7, 12, 2, -9, 13, -8],\n [0, 9, 7, -13, 8, 7],\n [0, 0, 13, -8, 6, 9],\n [0, 0, 0, 3, -15, 12],\n [0, 0, 0, 0, 8, -2],\n [0, 0, 0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
44
|
MATH
|
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-11, 3, 6, -7, 7, -4],\n [3, 2, -2, 4, -10, -14],\n [6, -2, 3, 6, 8, 5],\n [-7, 4, 6, 2, -10, -4],\n [7, -10, 8, -10, -6, 6],\n [-4, -14, 5, -4, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
27
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-11, -3, -7, 12, -3, -2],\n [-3, -4, -2, 1, 4, -2],\n [-7, -2, 1, 0, 4, 0],\n [12, 1, 0, 1, -3, 4],\n [-3, 4, 4, -3, -14, 2],\n [-2, -2, 0, 4, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
22
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-2, -13, 8, 6, 10, 3],\n [-13, 7, -8, -8, -2, 8],\n [8, -8, -12, 1, -8, -12],\n [6, -8, 1, -10, 8, 4],\n [10, -2, -8, 8, 5, 2],\n [3, 8, -12, 4, 2, -14]]\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[[-4, -3, 9, 5, -9, -6],\n [0, 1, 10, 5, 12, 14],\n [0, 0, -14, 12, 6, -5],\n [0, 0, 0, -12, 3, 10],\n [0, 0, 0, 0, -5, -12],\n [0, 0, 0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
42
|
MATH
|
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-14, 7, -1, 8, 6, 6],\n [0, 8, -15, 10, -12, -1],\n [0, 0, -13, 4, -5, 1],\n [0, 0, 0, -5, -14, -7],\n [0, 0, 0, 0, -7, -8],\n [0, 0, 0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
14
|
MATH
|
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-6, 9, -9, -13, -13, 2],\n [0, -4, -4, 3, 14, -10],\n [0, 0, 3, -11, -4, 11],\n [0, 0, 0, 1, -6, 9],\n [0, 0, 0, 0, 14, 0],\n [0, 0, 0, 0, 0, 1]]\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[[7, -1, 8, 0, -2, -8],\n [-1, 2, 1, -6, 4, 2],\n [8, 1, -3, 6, -5, -2],\n [0, -6, 6, 7, 4, 2],\n [-2, 4, -5, 4, -1, -2],\n [-8, 2, -2, 2, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
55
|
MATH
|
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[11, 7, 13, 2, 15, 14],\n [0, -9, -13, 2, 11, -6],\n [0, 0, -2, 15, 8, -13],\n [0, 0, 0, -14, -13, -11],\n [0, 0, 0, 0, 7, -4],\n [0, 0, 0, 0, 0, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
14
|
MATH
|
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[6, 3, -8, 0, -8, 7],\n [3, -6, -5, 6, -5, 6],\n [-8, -5, -14, 8, 12, 2],\n [0, 6, 8, -13, 12, 0],\n [-8, -5, 12, 12, 1, 6],\n [7, 6, 2, 0, 6, 8]]\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[[-4, -1, 9, -6, 14, 9],\n [0, -9, 4, -11, -15, 14],\n [0, 0, -3, -2, 8, 14],\n [0, 0, 0, 14, -11, 9],\n [0, 0, 0, 0, -1, -7],\n [0, 0, 0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
35
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[11, 11, -2, 2, 1, -4],\n [11, -10, -7, 6, 15, -4],\n [-2, -7, 14, -8, -4, 2],\n [2, 6, -8, 11, -2, -5],\n [1, 15, -4, -2, 3, 3],\n [-4, -4, 2, -5, 3, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
30
|
MATH
|
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-7, -5, 2, -1, 4, -1],\n [-5, -11, -4, -4, 8, 7],\n [2, -4, 4, -2, -6, 6],\n [-1, -4, -2, 2, -6, 12],\n [4, 8, -6, -6, -10, -5],\n [-1, 7, 6, 12, -5, -12]]\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[[-2, -11, -14, -5, -7, 8],\n [0, 11, 12, 13, -7, -13],\n [0, 0, -4, -6, -7, -1],\n [0, 0, 0, -5, 11, -14],\n [0, 0, 0, 0, -8, 11],\n [0, 0, 0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
11
|
MATH
|
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[12, 0, 0, 2, -2, 4],\n [0, 2, 1, 4, 8, 12],\n [0, 1, -13, 2, -4, -7],\n [2, 4, 2, -3, -12, -8],\n [-2, 8, -4, -12, 12, -9],\n [4, 12, -7, -8, -9, -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[[-3, 10, 1, -6, 2, 14],\n [10, -10, 11, -8, -4, -4],\n [1, 11, 9, -1, 2, -1],\n [-6, -8, -1, 5, 0, -12],\n [2, -4, 2, 0, -2, -3],\n [14, -4, -1, -12, -3, -2]]\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[[11, -6, -8, -6, -10, 8],\n [-6, 12, 6, 6, 0, -6],\n [-8, 6, 14, 2, 0, 2],\n [-6, 6, 2, 12, -6, 8],\n [-10, 0, 0, -6, 4, -8],\n [8, -6, 2, 8, -8, 6]]\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[[1, -6, 6, -15, 6, 10],\n [0, 11, 2, 2, -2, -1],\n [0, 0, -12, 11, -13, 4],\n [0, 0, 0, 13, -5, -15],\n [0, 0, 0, 0, -5, 10],\n [0, 0, 0, 0, 0, 13]]\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[[-12, 1, -13, -3, -7, -9],\n [0, 7, 13, 13, -5, 4],\n [0, 0, -2, 4, 6, -5],\n [0, 0, 0, 14, -4, 8],\n [0, 0, 0, 0, 0, -11],\n [0, 0, 0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
14
|
MATH
|
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[-13, 5, -4, 10, 12, -4],\n [5, -14, 4, -10, 3, 6],\n [-4, 4, 2, 6, -6, -4],\n [10, -10, 6, -2, 4, -6],\n [12, 3, -6, 4, 11, 6],\n [-4, 6, -4, -6, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
88
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[5, 3, 6, 0, -4, 0],\n [3, -1, 12, 7, 2, -6],\n [6, 12, -4, 6, -4, -3],\n [0, 7, 6, 12, 0, -1],\n [-4, 2, -4, 0, 8, -2],\n [0, -6, -3, -1, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
23
|
MATH
|
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[14, 2, -2, -1, 15, -10],\n [0, -3, 9, -15, 12, -10],\n [0, 0, -5, 6, 3, 8],\n [0, 0, 0, 9, -2, -1],\n [0, 0, 0, 0, 4, -15],\n [0, 0, 0, 0, 0, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
49
|
MATH
|
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[-15, -9, -8, -2, 3, -11],\n [-9, 4, 0, -4, -7, -12],\n [-8, 0, 10, -4, 12, -2],\n [-2, -4, -4, 7, -8, -4],\n [3, -7, 12, -8, 11, 2],\n [-11, -12, -2, -4, 2, -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[[2, -4, -8, -8, 2, 12],\n [0, 4, 14, -1, 11, 15],\n [0, 0, 4, 0, -12, -10],\n [0, 0, 0, 15, -13, 15],\n [0, 0, 0, 0, -5, 2],\n [0, 0, 0, 0, 0, 9]]\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[[-3, -4, 8, 3, -3, 6],\n [-4, -3, -2, 10, 10, 6],\n [8, -2, -4, -4, -8, 8],\n [3, 10, -4, 8, -2, 5],\n [-3, 10, -8, -2, -13, -1],\n [6, 6, 8, 5, -1, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
84
|
MATH
|
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-4, 7, 5, 3, 0, 0],\n [7, 8, 9, -4, -12, 2],\n [5, 9, 4, 2, -3, -2],\n [3, -4, 2, -12, 4, 4],\n [0, -12, -3, 4, -14, -4],\n [0, 2, -2, 4, -4, 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[[6, 2, -6, -8, -7, 7],\n [2, 5, -6, -8, -12, 12],\n [-6, -6, 0, 6, 2, -4],\n [-8, -8, 6, -14, 0, -6],\n [-7, -12, 2, 0, 14, 7],\n [7, 12, -4, -6, 7, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
94
|
MATH
|
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[9, 8, -12, 0, -8, -2],\n [8, 9, -1, 0, -10, 0],\n [-12, -1, 15, -9, -10, -5],\n [0, 0, -9, 7, 2, 6],\n [-8, -10, -10, 2, -2, 7],\n [-2, 0, -5, 6, 7, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
29
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-15, -13, 0, -4, -3, 0],\n [-13, 9, -2, 2, 6, 6],\n [0, -2, -1, -2, -7, -6],\n [-4, 2, -2, -4, 2, -1],\n [-3, 6, -7, 2, 11, 3],\n [0, 6, -6, -1, 3, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
27
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-11, -4, -2, 8, 0, -1],\n [-4, -10, -5, 5, -2, 2],\n [-2, -5, 3, 0, 2, 1],\n [8, 5, 0, 8, 6, -3],\n [0, -2, 2, 6, 13, 2],\n [-1, 2, 1, -3, 2, 2]]\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[[7, -4, -10, 4, 7, 14],\n [0, 4, 0, 2, -6, 12],\n [0, 0, 2, 5, -15, 7],\n [0, 0, 0, -11, -1, 6],\n [0, 0, 0, 0, 7, 10],\n [0, 0, 0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
11
|
MATH
|
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[10, 2, -8, -4, -6, -6],\n [2, -8, 6, -6, -5, -3],\n [-8, 6, 15, -4, -6, 2],\n [-4, -6, -4, 10, 14, 4],\n [-6, -5, -6, 14, -7, -11],\n [-6, -3, 2, 4, -11, 5]]\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, 14, -8, -1, -3, -9],\n [14, -10, -8, -8, -10, 6],\n [-8, -8, 2, -4, 1, -1],\n [-1, -8, -4, -15, 6, 6],\n [-3, -10, 1, 6, -1, -5],\n [-9, 6, -1, 6, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
92
|
MATH
|
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[12, 0, 0, -11, -6, 5],\n [0, -4, -6, -2, -8, -8],\n [0, -6, -2, 0, -1, -6],\n [-11, -2, 0, 10, -2, -7],\n [-6, -8, -1, -2, 13, 5],\n [5, -8, -6, -7, 5, -11]]\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[[-1, 2, -8, 0, -8, -2],\n [2, -10, -2, 0, -4, 8],\n [-8, -2, 5, 6, -1, 5],\n [0, 0, 6, 12, -1, -2],\n [-8, -4, -1, -1, -12, 2],\n [-2, 8, 5, -2, 2, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
19
|
MATH
|
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-12, 6, 0, 0, -6, 13],\n [6, -1, 0, -12, 4, -4],\n [0, 0, 14, 6, -9, 8],\n [0, -12, 6, 9, 4, 2],\n [-6, 4, -9, 4, -9, -1],\n [13, -4, 8, 2, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
85
|
MATH
|
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[13, 0, 2, -3, 7, -2],\n [0, -9, 0, -4, -6, 10],\n [2, 0, -1, 8, -2, 0],\n [-3, -4, 8, 6, 3, -8],\n [7, -6, -2, 3, 8, 9],\n [-2, 10, 0, -8, 9, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
76
|
MATH
|
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[1, 9, 10, -2, -8, 4],\n [9, 3, -5, 7, -12, -3],\n [10, -5, 3, -12, -10, -13],\n [-2, 7, -12, -1, 4, -7],\n [-8, -12, -10, 4, 5, -6],\n [4, -3, -13, -7, -6, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
106
|
MATH
|
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-9, 4, -8, 3, 3, -6],\n [4, 9, 10, 0, -1, -10],\n [-8, 10, 2, -10, -4, -2],\n [3, 0, -10, 1, -1, -6],\n [3, -1, -4, -1, -12, 4],\n [-6, -10, -2, -6, 4, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
22
|
MATH
|
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[-8, -10, -14, -12, -10, 2],\n [-10, -15, 4, -7, -2, -11],\n [-14, 4, 1, 12, -14, 9],\n [-12, -7, 12, 5, -1, -10],\n [-10, -2, -14, -1, -4, 0],\n [2, -11, 9, -10, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
33
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-4, -14, -10, 1, -13, -14],\n [0, 14, 4, -8, 6, -4],\n [0, 0, -11, -3, 13, 15],\n [0, 0, 0, 0, -6, 14],\n [0, 0, 0, 0, -4, 1],\n [0, 0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
14
|
MATH
|
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[14, -3, 7, 12, 3, -8],\n [0, -11, 4, -8, 8, -4],\n [0, 0, 14, 5, 4, -10],\n [0, 0, 0, -9, -15, 5],\n [0, 0, 0, 0, -14, 13],\n [0, 0, 0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
14
|
MATH
|
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-14, -7, 6, -14, 0, 2],\n [-7, -15, 2, -4, 4, 2],\n [6, 2, -12, -2, 0, -4],\n [-14, -4, -2, -1, 1, 4],\n [0, 4, 0, 1, -1, -6],\n [2, 2, -4, 4, -6, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
30
|
MATH
|
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[8, -3, 10, 0, -12, 1],\n [-3, -9, -4, -2, 1, -2],\n [10, -4, -14, 8, 0, -14],\n [0, -2, 8, 2, 0, 4],\n [-12, 1, 0, 0, -15, -6],\n [1, -2, -14, 4, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
27
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-2, 13, 4, -13, -13, -7],\n [0, 9, -3, 5, -14, -8],\n [0, 0, -12, 9, -1, -12],\n [0, 0, 0, 12, -3, 15],\n [0, 0, 0, 0, 12, 15],\n [0, 0, 0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
12
|
MATH
|
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[7, -6, 8, 5, 0, 2],\n [-6, -6, 11, -6, 14, 4],\n [8, 11, 15, 0, -2, -11],\n [5, -6, 0, -13, 4, -10],\n [0, 14, -2, 4, -9, -6],\n [2, 4, -11, -10, -6, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
92
|
MATH
|
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-8, 7, -4, 2, 5, 9],\n [7, 4, 2, 0, -10, -1],\n [-4, 2, -11, -2, 2, 0],\n [2, 0, -2, 11, 12, 10],\n [5, -10, 2, 12, 6, 0],\n [9, -1, 0, 10, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
75
|
MATH
|
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[6, 0, 2, 4, -2, 7],\n [0, 8, 0, -11, -2, 1],\n [2, 0, 2, -3, 0, 8],\n [4, -11, -3, -12, 8, 0],\n [-2, -2, 0, 8, 5, -4],\n [7, 1, 8, 0, -4, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
73
|
MATH
|
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[4, 0, 12, 2, -8, -13],\n [0, 13, 4, 13, -10, -6],\n [0, 0, -3, 1, -7, 1],\n [0, 0, 0, -15, -14, 12],\n [0, 0, 0, 0, 2, 10],\n [0, 0, 0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
44
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-14, -4, 7, -1, -12, 1],\n [-4, 1, 0, 2, 2, -7],\n [7, 0, -4, -12, 5, -4],\n [-1, 2, -12, 9, 8, 0],\n [-12, 2, 5, 8, -13, 0],\n [1, -7, -4, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
31
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MATH
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[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[15, 0, -1, -6, 10, -1],\n [0, -9, -4, 1, -2, -2],\n [-1, -4, -11, 6, -1, -10],\n [-6, 1, 6, 0, 10, 1],\n [10, -2, -1, 10, -7, -13],\n [-1, -2, -10, 1, -13, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
26
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MATH
|
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-12, -2, -7, -7, 9, 10],\n [0, 14, 15, 2, -6, 5],\n [0, 0, 11, -8, -14, 6],\n [0, 0, 0, 0, 12, -14],\n [0, 0, 0, 0, -8, 2],\n [0, 0, 0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
14
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MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[12, 12, 5, 4, 4, -2],\n [12, 4, 6, -6, 4, -2],\n [5, 6, 5, -6, 4, 3],\n [4, -6, -6, -4, 4, -2],\n [4, 4, 4, 4, 5, 2],\n [-2, -2, 3, -2, 2, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
62
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MATH
|
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