[User]
What is the largest eigenvalue by absolute value for the following matrix?
[[-1, 3, -2, 4, 12, 0],
 [3, 9, 8, -8, 1, 12],
 [-2, 8, -7, -7, 0, 10],
 [4, -8, -7, 8, -12, -2],
 [12, 1, 0, -12, -10, 4],
 [0, 12, 10, -2, 4, 5]]

Present the answer in LaTex format: \boxed{Your answer}

dataset: MATH


[User]
What is the largest eigenvalue by absolute value for the following matrix?
[[-2, 0, -7, 8, -11, -6],
 [0, -9, -6, -2, -4, -2],
 [-7, -6, -8, -10, -2, -6],
 [8, -2, -10, -10, -4, -11],
 [-11, -4, -2, -4, 8, -4],
 [-6, -2, -6, -11, -4, -3]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the largest eigenvalue by absolute value of the matrix:
[[9, -8, -4, -1, 11, 1],
 [-8, -14, 11, -2, -8, -2],
 [-4, 11, -1, 6, 6, -2],
 [-1, -2, 6, 3, 4, -1],
 [11, -8, 6, 4, 8, 10],
 [1, -2, -2, -1, 10, -8]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:
[[1, -14, 8, -15, 8, 4],
 [-14, 5, 6, 5, -8, -2],
 [8, 6, 2, 6, 10, 8],
 [-15, 5, 6, -2, -2, -9],
 [8, -8, 10, -2, 6, 0],
 [4, -2, 8, -9, 0, 12]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:
[[-6, -12, -2, -12, 10, -1],
 [-12, 9, 1, -4, 6, 4],
 [-2, 1, -2, -8, -6, 4],
 [-12, -4, -8, 2, 8, 4],
 [10, 6, -6, 8, 13, -6],
 [-1, 4, 4, 4, -6, 13]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:
[[-4, 15, 2, 2, -6, 11],
 [15, 0, 5, -12, -6, 4],
 [2, 5, 1, 12, 0, -2],
 [2, -12, 12, -13, -1, 4],
 [-6, -6, 0, -1, 1, -4],
 [11, 4, -2, 4, -4, 0]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:
[[10, -2, -6, 5, 0, -3],
 [-2, 4, 6, 0, 3, -7],
 [-6, 6, -3, 5, -10, -2],
 [5, 0, 5, 14, 6, -2],
 [0, 3, -10, 6, 0, 2],
 [-3, -7, -2, -2, 2, 12]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:
[[3, 2, -2, -6, -12, -2],
 [2, -7, 6, 3, -2, -2],
 [-2, 6, 15, 7, 2, -1],
 [-6, 3, 7, -3, 12, -2],
 [-12, -2, 2, 12, 12, -13],
 [-2, -2, -1, -2, -13, 12]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the largest eigenvalue by absolute value for the following matrix?
[[-6, 7, -12, -4, -3, 12],
 [7, 4, -2, 2, 10, -6],
 [-12, -2, 0, 1, -2, -2],
 [-4, 2, 1, -7, -8, -4],
 [-3, 10, -2, -8, 13, 8],
 [12, -6, -2, -4, 8, -11]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the largest eigenvalue by absolute value for the matrix:
[[2, 9, 6, 6, 6, -5],
 [9, 5, -2, -4, 0, 0],
 [6, -2, -15, -6, -2, 4],
 [6, -4, -6, 9, -2, -8],
 [6, 0, -2, -2, 7, -1],
 [-5, 0, 4, -8, -1, 2]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the largest eigenvalue by absolute value of the matrix:
[[-6, 0, -5, -10, 12, 6],
 [0, 8, -10, 4, -6, 8],
 [-5, -10, -10, -3, 10, -7],
 [-10, 4, -3, -3, 6, -2],
 [12, -6, 10, 6, 2, 2],
 [6, 8, -7, -2, 2, 1]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the sum of absolute values of all eigenvalues for the following matrix?
[[2, 12, 4, -10, 11, -7],
 [0, -10, 3, -14, -15, 14],
 [0, 0, -7, -6, -8, 11],
 [0, 0, 0, 10, -13, -2],
 [0, 0, 0, 0, 8, 11],
 [0, 0, 0, 0, 0, -14]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:
[[-5, 4, 0, 3, 0, 2],
 [4, 4, 7, 8, -8, -6],
 [0, 7, 3, 6, 6, 1],
 [3, 8, 6, -9, 0, 2],
 [0, -8, 6, 0, 7, -14],
 [2, -6, 1, 2, -14, 9]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:
[[-3, -2, -4, 0, 6, 2],
 [0, 4, -6, 10, -5, -3],
 [0, 0, -9, -12, 8, -9],
 [0, 0, 0, -1, -6, -14],
 [0, 0, 0, 0, 4, -1],
 [0, 0, 0, 0, 0, -4]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the largest eigenvalue by absolute value for the matrix:
[[15, 2, 2, 10, -5, -8],
 [2, 2, 0, -2, -8, 0],
 [2, 0, -10, -12, 0, 2],
 [10, -2, -12, 13, 3, -6],
 [-5, -8, 0, 3, 7, -11],
 [-8, 0, 2, -6, -11, 5]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:
[[-13, 3, 2, -8, 10, 2],
 [3, 6, 1, 2, -12, 7],
 [2, 1, -11, 0, -4, -2],
 [-8, 2, 0, 14, 10, -6],
 [10, -12, -4, 10, -15, -1],
 [2, 7, -2, -6, -1, -7]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:
[[-5, -7, -6, 0, -2, 6],
 [-7, 10, -4, -2, 0, 0],
 [-6, -4, -10, -4, 0, -2],
 [0, -2, -4, 15, -8, 10],
 [-2, 0, 0, -8, -7, 12],
 [6, 0, -2, 10, 12, -3]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the sum of absolute values of all eigenvalues for the following matrix?
[[-8, 6, -6, 4, -9, 5],
 [6, -9, 0, 4, -8, 12],
 [-6, 0, -3, -7, -1, -4],
 [4, 4, -7, 8, 0, 8],
 [-9, -8, -1, 0, -1, -4],
 [5, 12, -4, 8, -4, 1]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the largest eigenvalue by absolute value for the following matrix?
[[-14, 2, 6, -11, -4, -8],
 [2, -4, 4, 14, -6, 1],
 [6, 4, -6, -9, 0, 0],
 [-11, 14, -9, -14, -10, 0],
 [-4, -6, 0, -10, 12, -4],
 [-8, 1, 0, 0, -4, 8]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:
[[-13, -10, 0, -4, 6, 3],
 [-10, -1, 6, 2, 4, -3],
 [0, 6, 2, 2, -4, 2],
 [-4, 2, 2, -11, 4, 2],
 [6, 4, -4, 4, -11, 0],
 [3, -3, 2, 2, 0, 13]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the largest eigenvalue by absolute value of the matrix:
[[-2, -10, -4, -8, 12, 12],
 [-10, -4, 4, -4, 11, 6],
 [-4, 4, -11, 10, 4, 6],
 [-8, -4, 10, 14, 2, -2],
 [12, 11, 4, 2, -3, -4],
 [12, 6, 6, -2, -4, 5]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the sum of absolute values of all eigenvalues for the matrix:
[[-9, -3, 6, -8, 2, 2],
 [-3, -9, 0, 7, 6, 0],
 [6, 0, -4, -2, -5, -4],
 [-8, 7, -2, -3, -6, 4],
 [2, 6, -5, -6, 5, 4],
 [2, 0, -4, 4, 4, -8]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the largest eigenvalue by absolute value for the following matrix?
[[-6, -2, 11, -5, 10, -8],
 [-2, 7, 0, -4, -8, -8],
 [11, 0, 11, 0, -3, 0],
 [-5, -4, 0, -3, 0, 6],
 [10, -8, -3, 0, -13, -14],
 [-8, -8, 0, 6, -14, -7]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the sum of absolute values of all eigenvalues of the matrix:
[[11, 10, 10, 0, -2, 8],
 [10, 10, -10, -2, 2, -4],
 [10, -10, -1, 4, 2, -8],
 [0, -2, 4, -15, -2, -10],
 [-2, 2, 2, -2, -5, 11],
 [8, -4, -8, -10, 11, -12]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the largest eigenvalue by absolute value of the matrix:
[[-13, 1, 8, -10, -3, -2],
 [1, -7, 2, 0, 0, -10],
 [8, 2, -5, 1, 4, -2],
 [-10, 0, 1, -13, -6, -4],
 [-3, 0, 4, -6, 9, 8],
 [-2, -10, -2, -4, 8, -5]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the sum of absolute values of all eigenvalues for the matrix:
[[13, -8, 8, -2, -2, 0],
 [-8, -4, -10, 4, 0, 0],
 [8, -10, 5, 4, 13, -2],
 [-2, 4, 4, -6, -12, -8],
 [-2, 0, 13, -12, -15, 5],
 [0, 0, -2, -8, 5, -11]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the largest eigenvalue by absolute value of the matrix:
[[3, 10, -4, 8, 1, 4],
 [10, -4, -2, 1, 8, 10],
 [-4, -2, 3, 4, -6, 4],
 [8, 1, 4, 3, -4, -2],
 [1, 8, -6, -4, -9, -3],
 [4, 10, 4, -2, -3, 8]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the sum of absolute values of all eigenvalues of the matrix:
[[8, -6, 4, 5, 7, 8],
 [-6, 15, -6, -4, 8, 5],
 [4, -6, 15, 4, -1, 4],
 [5, -4, 4, -7, 5, 2],
 [7, 8, -1, 5, 7, -1],
 [8, 5, 4, 2, -1, 0]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the largest eigenvalue by absolute value for the matrix:
[[-1, -5, -6, -4, 10, -4],
 [-5, -7, 9, 2, -4, -12],
 [-6, 9, -14, 2, -10, 5],
 [-4, 2, 2, -9, -4, -8],
 [10, -4, -10, -4, 2, 6],
 [-4, -12, 5, -8, 6, 5]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the largest eigenvalue by absolute value for the matrix:
[[-4, 0, 7, 6, 2, 4],
 [0, -7, 12, 6, -6, -12],
 [7, 12, -14, -11, -2, -11],
 [6, 6, -11, -3, 1, -4],
 [2, -6, -2, 1, 9, 13],
 [4, -12, -11, -4, 13, -4]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the largest eigenvalue by absolute value for the matrix:
[[7, 7, 5, 15, -12, -9],
 [0, -13, 6, 9, -8, -15],
 [0, 0, -4, -4, -9, -13],
 [0, 0, 0, 7, -2, 5],
 [0, 0, 0, 0, 2, -3],
 [0, 0, 0, 0, 0, 6]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:
[[1, -12, 6, 10, -2, -5],
 [-12, -6, 6, 4, 8, 4],
 [6, 6, -5, 1, -3, -6],
 [10, 4, 1, 3, -1, -10],
 [-2, 8, -3, -1, 2, 13],
 [-5, 4, -6, -10, 13, -11]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:
[[7, -10, -8, 1, -14, 13],
 [0, 14, -9, -6, 5, -13],
 [0, 0, -15, 2, 4, -6],
 [0, 0, 0, -13, 15, -1],
 [0, 0, 0, 0, 0, -15],
 [0, 0, 0, 0, 0, 15]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the sum of absolute values of all eigenvalues of the matrix:
[[3, 4, -7, 0, -3, 2],
 [4, -3, -6, -8, 3, -12],
 [-7, -6, 5, -2, 4, 2],
 [0, -8, -2, -10, -3, 2],
 [-3, 3, 4, -3, -2, -5],
 [2, -12, 2, 2, -5, 6]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:
[[-4, -7, 4, 2, -10, -10],
 [-7, -4, -6, -9, -11, 8],
 [4, -6, -13, -2, -10, -4],
 [2, -9, -2, -9, 1, -6],
 [-10, -11, -10, 1, 2, 6],
 [-10, 8, -4, -6, 6, 15]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the largest eigenvalue by absolute value for the matrix:
[[-3, -10, -2, -6, 5, 4],
 [-10, -7, 14, -10, -11, -5],
 [-2, 14, -7, -13, 8, -4],
 [-6, -10, -13, 3, -3, -12],
 [5, -11, 8, -3, -14, 6],
 [4, -5, -4, -12, 6, 0]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the sum of absolute values of all eigenvalues for the following matrix?
[[-6, -3, -9, -11, 4, -2],
 [-3, -14, 2, -2, -10, 6],
 [-9, 2, -11, 10, 1, -2],
 [-11, -2, 10, 15, -13, 0],
 [4, -10, 1, -13, -3, -4],
 [-2, 6, -2, 0, -4, -12]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:
[[-1, -4, -2, -2, 13, 12],
 [-4, 5, -8, 4, -2, -4],
 [-2, -8, -12, -2, -4, 0],
 [-2, 4, -2, -2, -6, -2],
 [13, -2, -4, -6, 7, 4],
 [12, -4, 0, -2, 4, -12]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the sum of absolute values of all eigenvalues for the matrix:
[[11, 8, 2, 6, 6, 6],
 [8, -7, -9, 2, 1, 6],
 [2, -9, -14, 8, -7, -4],
 [6, 2, 8, -2, 4, -6],
 [6, 1, -7, 4, 8, 2],
 [6, 6, -4, -6, 2, -2]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:
[[-8, 4, 2, 11, -8, -4],
 [4, 7, 1, 0, -2, -4],
 [2, 1, 7, -6, 0, -8],
 [11, 0, -6, 9, -2, 4],
 [-8, -2, 0, -2, -6, -4],
 [-4, -4, -8, 4, -4, 5]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the largest eigenvalue by absolute value of the matrix:
[[3, 0, 7, -7, -2, -2],
 [0, 2, 10, -13, -3, 10],
 [0, 0, 14, -8, 10, -7],
 [0, 0, 0, 8, 2, 14],
 [0, 0, 0, 0, 7, 3],
 [0, 0, 0, 0, 0, -4]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the sum of absolute values of all eigenvalues for the matrix:
[[-14, 8, -4, 10, -6, 0],
 [8, 2, 4, -10, 3, -7],
 [-4, 4, 8, -6, -9, -10],
 [10, -10, -6, -11, -3, -1],
 [-6, 3, -9, -3, 4, -2],
 [0, -7, -10, -1, -2, 2]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:
[[-3, -5, 2, 0, -9, -2],
 [-5, -7, -14, 0, -2, 6],
 [2, -14, -14, 10, -4, 2],
 [0, 0, 10, 5, 2, 2],
 [-9, -2, -4, 2, 9, 2],
 [-2, 6, 2, 2, 2, 10]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the largest eigenvalue by absolute value for the matrix:
[[-13, -13, -1, 2, 11, -1],
 [0, -12, 4, -2, -8, -2],
 [0, 0, 0, 10, -7, 11],
 [0, 0, 0, 9, -13, 4],
 [0, 0, 0, 0, -6, 7],
 [0, 0, 0, 0, 0, 14]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the largest eigenvalue by absolute value for the following matrix?
[[14, 8, 3, 2, 3, 10],
 [8, 6, -6, 0, -6, -4],
 [3, -6, -12, -4, -3, -2],
 [2, 0, -4, 0, -5, -7],
 [3, -6, -3, -5, 15, -4],
 [10, -4, -2, -7, -4, -6]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:
[[6, 4, 2, -7, 2, -14],
 [4, -9, 10, 4, -2, 3],
 [2, 10, -10, 10, -2, 3],
 [-7, 4, 10, -12, -8, -3],
 [2, -2, -2, -8, 6, -12],
 [-14, 3, 3, -3, -12, 8]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the sum of absolute values of all eigenvalues of the matrix:
[[6, 5, 4, -15, -5, 7],
 [0, -4, 10, -13, 2, 8],
 [0, 0, 8, -14, 10, -8],
 [0, 0, 0, -8, 10, 5],
 [0, 0, 0, 0, -2, -4],
 [0, 0, 0, 0, 0, 11]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the largest eigenvalue by absolute value for the matrix:
[[-13, 0, 4, -10, -5, -4],
 [0, -13, 0, -10, 0, -4],
 [4, 0, -12, -10, 10, -6],
 [-10, -10, -10, 2, -4, -5],
 [-5, 0, 10, -4, -9, -4],
 [-4, -4, -6, -5, -4, 13]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the largest eigenvalue by absolute value for the matrix:
[[6, 2, -12, 0, 1, 2],
 [2, -4, -4, 1, -4, -10],
 [-12, -4, 6, -4, -12, -12],
 [0, 1, -4, 14, 12, -4],
 [1, -4, -12, 12, -1, -6],
 [2, -10, -12, -4, -6, -4]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the sum of absolute values of all eigenvalues for the matrix:
[[-8, -4, 0, 3, -4, -10],
 [-4, -3, 0, -12, -7, 10],
 [0, 0, -14, 2, -5, -6],
 [3, -12, 2, -3, 7, -10],
 [-4, -7, -5, 7, -2, -8],
 [-10, 10, -6, -10, -8, -15]]

Present the answer in LaTex format: \boxed{Your answer}