messages
list | ground_truth
string | dataset
string |
|---|---|---|
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[16, -21, 25, -15, -12, -33, -14, 17, -34, -6, 2, -34],\n [0, 24, -15, -3, 22, -14, 13, 23, 6, 24, -21, 26],\n [0, 0, 26, 15, 19, 28, -33, 15, -29, -15, 3, -18],\n [0, 0, 0, -27, 17, -34, 24, 35, 8, -28, 11, -1],\n [0, 0, 0, 0, -30, 18, -32, 18, 27, -18, 8, -2],\n [0, 0, 0, 0, 0, 4, 17, -12, -10, 24, 5, -7],\n [0, 0, 0, 0, 0, 0, -28, 27, -25, -28, -1, -1],\n [0, 0, 0, 0, 0, 0, 0, -3, 12, -13, 26, 1],\n [0, 0, 0, 0, 0, 0, 0, 0, -9, -27, -21, 6],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -23, -4, 35],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, -6],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
30
|
MATH
|
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[8, -12, 23, -4, 16, 26, 22, 16, -24, 3, -34, -33],\n [0, 23, -34, -34, 18, -35, -17, -34, 17, 8, -4, 34],\n [0, 0, 19, 20, -19, 2, -12, 33, 34, -25, -20, 23],\n [0, 0, 0, 23, 0, -17, 31, -17, -16, 35, 16, -3],\n [0, 0, 0, 0, 21, 14, -13, -5, 6, -29, -20, 24],\n [0, 0, 0, 0, 0, 1, -4, -27, -17, 12, -33, -16],\n [0, 0, 0, 0, 0, 0, -11, -18, 30, 18, -1, 25],\n [0, 0, 0, 0, 0, 0, 0, -16, -28, -29, 31, -19],\n [0, 0, 0, 0, 0, 0, 0, 0, -28, -9, -9, -15],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 28, 13, -19],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -3],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
212
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-9, -23, -20, 5, -28, 14, -4, 18, 11, -17, 9, -20],\n [-23, -23, 27, -6, 16, 10, 17, -2, 2, -7, -6, 5],\n [-20, 27, -4, 16, 17, 8, 25, 26, 4, -8, 15, 22],\n [5, -6, 16, 34, -8, 2, 26, 2, 20, 10, -19, 12],\n [-28, 16, 17, -8, 16, -24, 5, -13, -26, -11, 2, -8],\n [14, 10, 8, 2, -24, -24, -24, 17, -1, 12, -6, -25],\n [-4, 17, 25, 26, 5, -24, 31, -4, -26, 15, 16, -4],\n [18, -2, 26, 2, -13, 17, -4, -3, -16, -10, 0, -14],\n [11, 2, 4, 20, -26, -1, -26, -16, -12, -29, -2, -12],\n [-17, -7, -8, 10, -11, 12, 15, -10, -29, 31, 0, 12],\n [9, -6, 15, -19, 2, -6, 16, 0, -2, 0, -10, 6],\n [-20, 5, 22, 12, -8, -25, -4, -14, -12, 12, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
100
|
MATH
|
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[-12, -13, 26, 1, -24, 19, -23, -13, -6, -19, 26, -23],\n [0, -17, 13, -24, 25, -17, -27, 35, -8, 16, -20, 33],\n [0, 0, 16, 17, -13, -20, 21, 3, 17, 6, 22, 3],\n [0, 0, 0, -18, -27, 22, -19, -29, 10, -23, 4, 6],\n [0, 0, 0, 0, -31, -7, 1, 2, -28, 29, -19, 35],\n [0, 0, 0, 0, 0, -17, 25, 18, 3, -17, 3, 31],\n [0, 0, 0, 0, 0, 0, -35, -33, 26, 27, -11, 20],\n [0, 0, 0, 0, 0, 0, 0, 9, 25, 11, -15, 0],\n [0, 0, 0, 0, 0, 0, 0, 0, -5, -35, 18, -33],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 22, 24, 14],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -30],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13]]\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[[-25, -20, 28, -4, -8, -3, -18, -25, -1, -4, -32, 7],\n [-20, -33, 6, 4, 16, -9, -26, -33, 12, 12, -22, 2],\n [28, 6, -2, -8, 8, 16, 19, -14, 2, -6, 6, 4],\n [-4, 4, -8, 11, 2, -12, 10, 20, -4, 24, 2, 23],\n [-8, 16, 8, 2, 2, -18, 23, -22, 2, -27, -24, -3],\n [-3, -9, 16, -12, -18, 17, 30, -4, 4, 6, 4, 2],\n [-18, -26, 19, 10, 23, 30, -9, 15, 20, -4, 4, -18],\n [-25, -33, -14, 20, -22, -4, 15, -35, -10, -17, 6, -2],\n [-1, 12, 2, -4, 2, 4, 20, -10, 25, -16, 10, -32],\n [-4, 12, -6, 24, -27, 6, -4, -17, -16, 23, 0, -12],\n [-32, -22, 6, 2, -24, 4, 4, 6, 10, 0, 8, -2],\n [7, 2, 4, 23, -3, 2, -18, -2, -32, -12, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
101
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-30, 25, -11, 18, 26, 14, 11, 10, -18, 3, -4, -9],\n [25, 34, -31, 17, 14, -23, 16, -2, -14, -12, 16, 16],\n [-11, -31, 30, -32, -14, -4, 30, 24, 6, 1, -16, 22],\n [18, 17, -32, 34, -18, 18, 4, -20, -10, 14, -21, -24],\n [26, 14, -14, -18, -33, -18, -3, -4, -12, -8, -8, -28],\n [14, -23, -4, 18, -18, 29, 20, 2, -24, -9, -10, 2],\n [11, 16, 30, 4, -3, 20, -27, -4, -2, -10, 2, 2],\n [10, -2, 24, -20, -4, 2, -4, -1, 8, 2, -8, 10],\n [-18, -14, 6, -10, -12, -24, -2, 8, 2, -22, 14, -5],\n [3, -12, 1, 14, -8, -9, -10, 2, -22, 31, -4, 16],\n [-4, 16, -16, -21, -8, -10, 2, -8, 14, -4, -9, 20],\n [-9, 16, 22, -24, -28, 2, 2, 10, -5, 16, 20, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
111
|
MATH
|
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[-7, -28, -31, -7, 11, 32, 9, -34, -9, 0, 0, -10],\n [0, -9, 33, -16, -25, 2, -30, -13, 11, 10, -24, -23],\n [0, 0, 7, 32, -31, 1, -5, -27, 15, -7, 4, 5],\n [0, 0, 0, 10, -15, 0, 18, 21, -35, 27, 18, 19],\n [0, 0, 0, 0, 17, -27, 16, 21, -10, 5, -1, 27],\n [0, 0, 0, 0, 0, -19, 7, 23, 15, 18, -12, -11],\n [0, 0, 0, 0, 0, 0, 27, -14, -10, -8, 13, 35],\n [0, 0, 0, 0, 0, 0, 0, -23, 15, 20, 26, -4],\n [0, 0, 0, 0, 0, 0, 0, 0, -18, -35, 11, 30],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -26, -2],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 31, 15],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
31
|
MATH
|
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-29, 2, 2, 4, -13, 4, -12, -5, 6, -26, -6, -6],\n [2, -16, -18, -20, 26, -7, -6, -16, 2, 12, -18, -6],\n [2, -18, -6, 12, -14, 0, -10, 7, -6, 2, -21, -18],\n [4, -20, 12, 34, -24, -14, 2, 14, -18, -4, 6, 0],\n [-13, 26, -14, -24, 4, -3, 20, 12, -9, -8, -12, 6],\n [4, -7, 0, -14, -3, 29, 9, 24, 8, 8, -16, -6],\n [-12, -6, -10, 2, 20, 9, 18, 12, -18, -21, 6, 1],\n [-5, -16, 7, 14, 12, 24, 12, -19, -26, 5, 21, 14],\n [6, 2, -6, -18, -9, 8, -18, -26, 8, 28, -3, 3],\n [-26, 12, 2, -4, -8, 8, -21, 5, 28, -11, -18, -22],\n [-6, -18, -21, 6, -12, -16, 6, 21, -3, -18, -10, -17],\n [-6, -6, -18, 0, 6, -6, 1, 14, 3, -22, -17, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
468
|
MATH
|
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[24, 3, -15, 15, 18, 12, 18, 14, 5, -15, 8, -6],\n [3, -20, 8, 22, 18, 16, 10, -4, -15, -27, 2, 0],\n [-15, 8, -7, -4, 2, 16, -8, 17, -26, 3, 10, -27],\n [15, 22, -4, 9, -4, -16, 0, 4, 28, -8, 4, 10],\n [18, 18, 2, -4, 32, 1, -4, -9, 7, 20, 19, 10],\n [12, 16, 16, -16, 1, -11, 2, -8, -13, 12, -6, 16],\n [18, 10, -8, 0, -4, 2, -31, 7, -8, 18, -15, 6],\n [14, -4, 17, 4, -9, -8, 7, -23, 18, -5, -28, 6],\n [5, -15, -26, 28, 7, -13, -8, 18, -11, -20, -21, 12],\n [-15, -27, 3, -8, 20, 12, 18, -5, -20, 33, 4, 16],\n [8, 2, 10, 4, 19, -6, -15, -28, -21, 4, 23, -3],\n [-6, 0, -27, 10, 10, 16, 6, 6, 12, 16, -3, -31]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
82
|
MATH
|
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[9, -1, 15, -14, -12, -24, -10, 8, -12, 14, 11, -14],\n [-1, 3, 28, -21, 2, -3, -4, 24, 22, -17, 0, -17],\n [15, 28, -8, -1, -12, -18, 28, -8, 2, 6, -22, -24],\n [-14, -21, -1, 29, -8, 4, -26, 28, 1, 2, 14, 16],\n [-12, 2, -12, -8, -30, -6, -1, 6, 0, -6, -11, -14],\n [-24, -3, -18, 4, -6, -4, -6, 0, 0, -10, 6, 0],\n [-10, -4, 28, -26, -1, -6, 33, -28, 0, 28, 15, -6],\n [8, 24, -8, 28, 6, 0, -28, -18, -27, -14, 13, 3],\n [-12, 22, 2, 1, 0, 0, 0, -27, 28, -10, 6, 3],\n [14, -17, 6, 2, -6, -10, 28, -14, -10, 2, -6, 4],\n [11, 0, -22, 14, -11, 6, 15, 13, 6, -6, 9, -3],\n [-14, -17, -24, 16, -14, 0, -6, 3, 3, 4, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
508
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[-4, -10, -16, -14, 16, -20, 0, -2, 18, -10, -22, 10],\n [-10, 25, 0, -20, -22, -8, 4, -6, -13, 22, 0, 14],\n [-16, 0, -30, 16, -14, -8, -9, 4, 14, -9, -30, -6],\n [-14, -20, 16, -17, 10, 16, -14, 1, 22, 8, -8, 8],\n [16, -22, -14, 10, 20, 24, -2, -14, 12, 12, 1, 24],\n [-20, -8, -8, 16, 24, -12, -9, -4, -27, -4, -2, -10],\n [0, 4, -9, -14, -2, -9, 0, -29, -16, -4, 14, -27],\n [-2, -6, 4, 1, -14, -4, -29, 6, 21, -6, -34, 13],\n [18, -13, 14, 22, 12, -27, -16, 21, -19, -6, 26, -8],\n [-10, 22, -9, 8, 12, -4, -4, -6, -6, -25, 1, -2],\n [-22, 0, -30, -8, 1, -2, 14, -34, 26, 1, -8, 1],\n [10, 14, -6, 8, 24, -10, -27, 13, -8, -2, 1, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
540
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[-10, 0, -13, 3, 6, 0, 31, 4, 14, -22, -12, -6],\n [0, 14, 4, 8, 10, 8, 21, -6, -6, -2, -2, -5],\n [-13, 4, 14, -24, -12, 2, -14, -32, 10, -1, 10, -2],\n [3, 8, -24, -10, 2, -10, -2, 11, -12, -10, -9, -5],\n [6, 10, -12, 2, 26, 6, 6, 23, 17, -12, -12, 24],\n [0, 8, 2, -10, 6, 34, 0, 8, -12, 25, 8, 3],\n [31, 21, -14, -2, 6, 0, -3, 24, 16, -4, -12, 25],\n [4, -6, -32, 11, 23, 8, 24, -8, 0, -17, -15, -12],\n [14, -6, 10, -12, 17, -12, 16, 0, 7, -16, -16, 18],\n [-22, -2, -1, -10, -12, 25, -4, -17, -16, -2, -1, 11],\n [-12, -2, 10, -9, -12, 8, -12, -15, -16, -1, 13, -6],\n [-6, -5, -2, -5, 24, 3, 25, -12, 18, 11, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
454
|
MATH
|
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[32, -28, 21, -12, 4, 8, 18, 0, -7, -20, -16, 8],\n [-28, -21, -12, 4, -20, 4, -22, -16, 32, -7, -8, -15],\n [21, -12, -18, -19, -9, 11, 28, 22, 4, -18, -18, -12],\n [-12, 4, -19, -1, 33, -2, -28, -30, 16, -16, -16, 30],\n [4, -20, -9, 33, 6, 2, 6, -2, 22, 2, -20, 26],\n [8, 4, 11, -2, 2, -33, -18, 0, 16, 10, -12, -8],\n [18, -22, 28, -28, 6, -18, -4, -8, -17, -8, 9, 4],\n [0, -16, 22, -30, -2, 0, -8, -6, -4, 8, 19, 4],\n [-7, 32, 4, 16, 22, 16, -17, -4, -20, -15, -26, -6],\n [-20, -7, -18, -16, 2, 10, -8, 8, -15, -15, 32, -18],\n [-16, -8, -18, -16, -20, -12, 9, 19, -26, 32, 31, 20],\n [8, -15, -12, 30, 26, -8, 4, 4, -6, -18, 20, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
596
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[13, -8, 0, -3, 12, -20, -19, -20, 0, -5, 22, -18],\n [-8, -15, 0, 31, -4, -13, -6, -24, 9, 10, -15, 5],\n [0, 0, -22, 9, -6, 15, -26, 20, -26, 10, -25, -15],\n [-3, 31, 9, 32, 2, 10, -4, -18, -3, -4, -6, -23],\n [12, -4, -6, 2, 7, -7, 20, 3, 2, -8, -18, -2],\n [-20, -13, 15, 10, -7, -27, -8, -21, 11, -6, -27, -10],\n [-19, -6, -26, -4, 20, -8, 2, 20, 14, 10, 25, -24],\n [-20, -24, 20, -18, 3, -21, 20, -15, 4, -12, 17, 14],\n [0, 9, -26, -3, 2, 11, 14, 4, -25, 16, -11, 12],\n [-5, 10, 10, -4, -8, -6, 10, -12, 16, -15, -10, 5],\n [22, -15, -25, -6, -18, -27, 25, 17, -11, -10, 22, 10],\n [-18, 5, -15, -23, -2, -10, -24, 14, 12, 5, 10, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
532
|
MATH
|
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[29, -16, -10, -30, -6, 2, -1, -16, -18, -21, -18, 5],\n [-16, -25, 9, -18, -25, 1, -7, 15, -14, -23, -15, 9],\n [-10, 9, -28, -6, 6, 0, 9, 0, -6, 21, 11, 14],\n [-30, -18, -6, -24, -15, -14, 2, 2, -24, -6, -10, -4],\n [-6, -25, 6, -15, -18, 11, -12, 12, 4, 12, -6, -10],\n [2, 1, 0, -14, 11, -24, 2, 4, -18, -9, 10, -13],\n [-1, -7, 9, 2, -12, 2, -23, -7, -21, -4, 6, 12],\n [-16, 15, 0, 2, 12, 4, -7, -33, -2, -22, 4, -20],\n [-18, -14, -6, -24, 4, -18, -21, -2, -33, 14, -32, 26],\n [-21, -23, 21, -6, 12, -9, -4, -22, 14, 22, -7, -2],\n [-18, -15, 11, -10, -6, 10, 6, 4, -32, -7, -16, -8],\n [5, 9, 14, -4, -10, -13, 12, -20, 26, -2, -8, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
108
|
MATH
|
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-19, 35, -32, -22, -33, 22, 19, -32, -12, -2, -6, -17],\n [0, 24, 24, -17, 13, 27, -14, -12, -6, 22, -5, 28],\n [0, 0, 9, 19, 19, -18, 27, 11, 21, 9, -3, -19],\n [0, 0, 0, 11, -21, 34, 11, -27, -20, 33, 25, -26],\n [0, 0, 0, 0, -17, 6, -1, 10, -10, 33, 28, 1],\n [0, 0, 0, 0, 0, -32, 3, -1, -35, -12, 21, 34],\n [0, 0, 0, 0, 0, 0, -5, -12, 0, -6, -12, -6],\n [0, 0, 0, 0, 0, 0, 0, 34, 8, 9, 20, 21],\n [0, 0, 0, 0, 0, 0, 0, 0, -16, -21, 12, 35],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -33, 1, 13],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 25, 25],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
259
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-14, 21, 30, -20, 15, 3, 4, 2, 24, 23, -26, 28],\n [0, 13, 28, -4, -29, -15, -16, -10, 32, -21, -22, -9],\n [0, 0, -8, -10, 27, 30, -11, -33, 8, 6, -30, 3],\n [0, 0, 0, 7, -17, 33, 15, -25, -24, -28, -12, 5],\n [0, 0, 0, 0, -21, 12, 6, 24, 34, -24, -34, -29],\n [0, 0, 0, 0, 0, -35, -28, -4, 12, -32, 34, -17],\n [0, 0, 0, 0, 0, 0, -35, 27, -15, -6, -23, -2],\n [0, 0, 0, 0, 0, 0, 0, 32, -11, -16, -2, -10],\n [0, 0, 0, 0, 0, 0, 0, 0, 30, 11, -33, -6],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 11, 22, 21],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 30],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
35
|
MATH
|
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[11, 2, -21, 27, -15, 21, 17, 10, -22, -19, 3, -27],\n [0, -13, 23, 10, 2, -22, 26, -1, -17, -6, -11, 4],\n [0, 0, -14, 12, 15, -33, 6, -17, -8, 9, 35, 27],\n [0, 0, 0, 2, 17, 25, 0, 4, -6, -27, 28, -3],\n [0, 0, 0, 0, 5, 32, 32, -28, -34, 5, 19, -20],\n [0, 0, 0, 0, 0, -25, 28, 14, -15, 33, 12, -16],\n [0, 0, 0, 0, 0, 0, -1, 29, -28, 9, 11, 4],\n [0, 0, 0, 0, 0, 0, 0, -14, -15, 15, 2, -16],\n [0, 0, 0, 0, 0, 0, 0, 0, 9, 31, 30, -2],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -9, -28, 29],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 26],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
25
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-19, -20, -6, 3, -10, -8, 4, 17, -12, 6, -14, -24],\n [-20, 10, -1, -22, 10, -6, 8, -16, 22, -5, 10, 12],\n [-6, -1, 10, -1, 7, -6, -2, -5, 11, 28, 8, -4],\n [3, -22, -1, -21, -2, 1, -8, 16, -3, 6, 22, -8],\n [-10, 10, 7, -2, -33, 32, -14, -4, -14, -17, -12, 16],\n [-8, -6, -6, 1, 32, 19, 4, 6, 22, -2, -22, 2],\n [4, 8, -2, -8, -14, 4, 9, 14, -2, 0, 5, 22],\n [17, -16, -5, 16, -4, 6, 14, -4, 20, 5, 10, -14],\n [-12, 22, 11, -3, -14, 22, -2, 20, 29, 16, 2, 4],\n [6, -5, 28, 6, -17, -2, 0, 5, 16, 28, 28, -24],\n [-14, 10, 8, 22, -12, -22, 5, 10, 2, 28, 31, 2],\n [-24, 12, -4, -8, 16, 2, 22, -14, 4, -24, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
93
|
MATH
|
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[1, 20, -8, -24, 22, -18, 4, 27, 8, -18, -18, 2],\n [20, 1, 10, -11, -13, 4, 16, -5, 17, -16, 8, 4],\n [-8, 10, -25, 2, -25, 20, 2, 5, -20, 2, -21, -1],\n [-24, -11, 2, -8, -28, -2, 6, -20, 29, 5, -5, -12],\n [22, -13, -25, -28, -31, 27, -24, 8, 8, -15, 2, -12],\n [-18, 4, 20, -2, 27, 19, -16, 26, -12, -25, 8, -2],\n [4, 16, 2, 6, -24, -16, -1, 4, 4, 7, -4, -10],\n [27, -5, 5, -20, 8, 26, 4, -14, 14, 30, 9, -1],\n [8, 17, -20, 29, 8, -12, 4, 14, -6, 10, 5, 4],\n [-18, -16, 2, 5, -15, -25, 7, 30, 10, -11, 16, -18],\n [-18, 8, -21, -5, 2, 8, -4, 9, 5, 16, 27, -2],\n [2, 4, -1, -12, -12, -2, -10, -1, 4, -18, -2, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
556
|
MATH
|
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-20, 30, 4, -19, -2, -20, 24, 30, 30, -23, 20, -5],\n [0, 3, 31, -28, 19, -9, 17, 3, 29, -19, -6, 17],\n [0, 0, -17, 17, -17, 21, -11, -5, 19, -13, -4, 26],\n [0, 0, 0, -16, -4, -22, 14, -8, 17, -12, -14, -6],\n [0, 0, 0, 0, -24, -5, -2, 13, 21, -10, -18, 2],\n [0, 0, 0, 0, 0, 8, 28, -7, -8, -25, 29, -17],\n [0, 0, 0, 0, 0, 0, 15, -23, 13, 34, 20, 15],\n [0, 0, 0, 0, 0, 0, 0, -26, 11, -13, -15, -23],\n [0, 0, 0, 0, 0, 0, 0, 0, -24, 1, 6, -19],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -34, -20, -27],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -33, -8],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
238
|
MATH
|
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-26, 8, 0, -9, 6, -10, -17, 12, -10, -34, -5, -16],\n [8, -11, -26, -15, -26, 19, -19, 7, -7, -20, 22, 26],\n [0, -26, 11, 10, 0, 16, 8, 17, 18, -15, 14, -24],\n [-9, -15, 10, 19, 22, -25, -2, -14, -18, 8, -3, 11],\n [6, -26, 0, 22, -32, 14, 5, 2, 1, 2, -3, 2],\n [-10, 19, 16, -25, 14, -8, 9, -14, 28, 24, -2, -6],\n [-17, -19, 8, -2, 5, 9, -8, -1, -8, -7, -1, -5],\n [12, 7, 17, -14, 2, -14, -1, 16, 10, -6, -2, -10],\n [-10, -7, 18, -18, 1, 28, -8, 10, 26, 30, 14, -26],\n [-34, -20, -15, 8, 2, 24, -7, -6, 30, 5, -15, 30],\n [-5, 22, 14, -3, -3, -2, -1, -2, 14, -15, -30, -12],\n [-16, 26, -24, 11, 2, -6, -5, -10, -26, 30, -12, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
536
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[23, 8, -27, 1, 0, -8, 6, 7, 6, 30, 19, 12],\n [0, -9, 31, -23, 9, -26, -27, 18, -9, -2, -35, -4],\n [0, 0, -16, -1, -19, -18, 9, 17, 32, 29, -35, 22],\n [0, 0, 0, 23, 5, -31, 29, -19, -14, 5, 32, 33],\n [0, 0, 0, 0, -10, -17, 24, 35, 11, 35, -10, 4],\n [0, 0, 0, 0, 0, -28, 5, -17, 10, -8, 32, -21],\n [0, 0, 0, 0, 0, 0, 27, 25, 0, -12, -12, -32],\n [0, 0, 0, 0, 0, 0, 0, 17, 26, 5, 21, 24],\n [0, 0, 0, 0, 0, 0, 0, 0, -33, 15, 11, 32],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -11, -9, 15],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, -4],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
232
|
MATH
|
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[27, 15, 0, 30, -21, 3, 34, -35, -13, 3, 21, -2],\n [0, -23, 34, -30, 16, -33, 27, 13, 11, 19, 28, 29],\n [0, 0, -4, 32, -18, 7, -1, 22, -3, -22, -2, 25],\n [0, 0, 0, -30, 13, 4, 29, 33, -9, -30, -23, 28],\n [0, 0, 0, 0, 32, 8, -13, -34, -14, 21, -29, 20],\n [0, 0, 0, 0, 0, -31, -9, -24, -19, -30, -31, 21],\n [0, 0, 0, 0, 0, 0, -17, 33, 30, 11, 3, 32],\n [0, 0, 0, 0, 0, 0, 0, -16, -7, -12, 27, 21],\n [0, 0, 0, 0, 0, 0, 0, 0, -8, 26, 5, 33],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -14, -10],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 17],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
32
|
MATH
|
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[32, 9, 0, -17, 10, 27, -2, 18, -6, -25, 9, 6],\n [9, -8, 12, -6, 10, -2, -10, -2, 11, -16, -25, 5],\n [0, 12, -4, -31, 14, 12, 5, -22, 20, 4, 12, -8],\n [-17, -6, -31, -9, 0, -10, -24, 16, -14, -12, 2, 12],\n [10, 10, 14, 0, 27, 6, 11, 17, -16, -6, 22, -8],\n [27, -2, 12, -10, 6, 12, -28, 13, 4, 18, 5, 14],\n [-2, -10, 5, -24, 11, -28, 3, 14, 5, 24, -5, -7],\n [18, -2, -22, 16, 17, 13, 14, 0, 16, -4, 6, 4],\n [-6, 11, 20, -14, -16, 4, 5, 16, -35, 9, -4, 2],\n [-25, -16, 4, -12, -6, 18, 24, -4, 9, 32, 30, -5],\n [9, -25, 12, 2, 22, 5, -5, 6, -4, 30, 16, -19],\n [6, 5, -8, 12, -8, 14, -7, 4, 2, -5, -19, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
546
|
MATH
|
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-1, 0, -4, -11, -33, -8, 19, 0, 16, 7, 12, -6],\n [0, 10, -20, 10, -10, 32, -20, -2, -10, 5, 6, -8],\n [-4, -20, 0, -2, 2, -18, -15, 23, 2, -6, 9, -6],\n [-11, 10, -2, 26, -2, 22, -2, 2, 6, 12, -9, -26],\n [-33, -10, 2, -2, 13, 30, 10, -12, 9, 0, 2, 28],\n [-8, 32, -18, 22, 30, -29, 6, 22, 14, 6, 10, -5],\n [19, -20, -15, -2, 10, 6, -20, -3, 24, 10, -7, 28],\n [0, -2, 23, 2, -12, 22, -3, 9, -24, -1, 0, 10],\n [16, -10, 2, 6, 9, 14, 24, -24, -14, -32, 17, 11],\n [7, 5, -6, 12, 0, 6, 10, -1, -32, 18, 0, 16],\n [12, 6, 9, -9, 2, 10, -7, 0, 17, 0, -5, 16],\n [-6, -8, -6, -26, 28, -5, 28, 10, 11, 16, 16, -7]]\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[[23, 30, -2, -14, -10, 28, 8, -12, -10, -13, 8, -16],\n [30, 6, -14, 28, -3, -20, 0, 2, -14, 28, -2, 5],\n [-2, -14, -26, 5, -28, -18, -10, 4, -6, 4, 22, 14],\n [-14, 28, 5, 31, 6, -33, -10, -4, -10, -15, -8, -20],\n [-10, -3, -28, 6, 34, 10, 5, -24, -24, -8, 30, -18],\n [28, -20, -18, -33, 10, 10, 8, -4, -8, 14, 25, -6],\n [8, 0, -10, -10, 5, 8, 12, -16, -10, 3, 15, 0],\n [-12, 2, 4, -4, -24, -4, -16, -1, 21, 5, -6, 10],\n [-10, -14, -6, -10, -24, -8, -10, 21, 22, -13, 24, -22],\n [-13, 28, 4, -15, -8, 14, 3, 5, -13, -11, -16, 2],\n [8, -2, 22, -8, 30, 25, 15, -6, 24, -16, -24, 16],\n [-16, 5, 14, -20, -18, -6, 0, 10, -22, 2, 16, 18]]\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[[-15, -6, -14, 12, 16, 20, 0, 16, 20, 22, -6, 4],\n [-6, -14, -2, 0, 2, -7, 10, 9, -2, 24, 13, 2],\n [-14, -2, 2, -14, -18, 2, 0, 25, -11, 23, 24, 2],\n [12, 0, -14, 7, -2, 0, -15, -10, 2, 11, 20, -22],\n [16, 2, -18, -2, 23, -2, -2, -17, 4, -14, -6, -2],\n [20, -7, 2, 0, -2, 13, -2, 28, -13, -2, -16, -26],\n [0, 10, 0, -15, -2, -2, -26, -16, 22, -16, -28, 2],\n [16, 9, 25, -10, -17, 28, -16, 20, 13, -9, 8, -12],\n [20, -2, -11, 2, 4, -13, 22, 13, -14, -5, -12, 1],\n [22, 24, 23, 11, -14, -2, -16, -9, -5, 26, -8, 18],\n [-6, 13, 24, 20, -6, -16, -28, 8, -12, -8, -19, -10],\n [4, 2, 2, -22, -2, -26, 2, -12, 1, 18, -10, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
497
|
MATH
|
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[35, -5, -26, -12, 2, 13, 8, 20, 28, -11, -24, 20],\n [-5, 18, -23, 18, 4, -14, 21, -4, 4, 22, 26, 7],\n [-26, -23, 2, 26, 10, -14, 0, -9, -4, 20, 2, 10],\n [-12, 18, 26, 16, -15, -6, -18, -30, -24, 11, 18, 18],\n [2, 4, 10, -15, -21, 3, 2, 9, -3, -8, -13, 22],\n [13, -14, -14, -6, 3, -20, -8, -20, -12, -5, -11, 14],\n [8, 21, 0, -18, 2, -8, 16, -15, -4, 3, 24, -18],\n [20, -4, -9, -30, 9, -20, -15, 21, -12, 10, 20, -30],\n [28, 4, -4, -24, -3, -12, -4, -12, -13, 24, -12, 10],\n [-11, 22, 20, 11, -8, -5, 3, 10, 24, -8, -10, -9],\n [-24, 26, 2, 18, -13, -11, 24, 20, -12, -10, 22, -10],\n [20, 7, 10, 18, 22, 14, -18, -30, 10, -9, -10, 27]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
101
|
MATH
|
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[-32, -4, 4, -16, 7, 24, 5, -3, -4, -12, 22, -22],\n [-4, -16, 18, -30, 21, -22, -18, -2, -3, 8, -17, -10],\n [4, 18, -10, -2, 15, 16, -24, -6, 19, -1, -18, 4],\n [-16, -30, -2, 13, 4, 10, -9, 1, 10, 4, -12, -27],\n [7, 21, 15, 4, -15, -6, 28, 18, -8, -18, 14, -2],\n [24, -22, 16, 10, -6, 20, 26, -1, 2, -28, -1, 16],\n [5, -18, -24, -9, 28, 26, 25, 24, 0, 8, -9, -13],\n [-3, -2, -6, 1, 18, -1, 24, 27, 0, 2, -22, -16],\n [-4, -3, 19, 10, -8, 2, 0, 0, 2, 16, 2, 13],\n [-12, 8, -1, 4, -18, -28, 8, 2, 16, -30, 28, 10],\n [22, -17, -18, -12, 14, -1, -9, -22, 2, 28, 28, -10],\n [-22, -10, 4, -27, -2, 16, -13, -16, 13, 10, -10, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
558
|
MATH
|
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-16, -1, -4, 12, 8, -12, 25, -19, 35, 14, 29, -4],\n [0, -23, 34, 22, -22, 1, 32, 4, 23, -20, 26, -32],\n [0, 0, 30, -5, -33, -28, -12, -21, 7, -5, 9, 30],\n [0, 0, 0, -6, -18, 33, 3, 24, 7, 9, -13, 33],\n [0, 0, 0, 0, -30, -4, -18, -21, 4, -30, 27, 31],\n [0, 0, 0, 0, 0, 32, 5, -31, -4, 34, -1, -14],\n [0, 0, 0, 0, 0, 0, -22, -18, -13, 11, 33, 11],\n [0, 0, 0, 0, 0, 0, 0, 12, -26, -25, -15, 9],\n [0, 0, 0, 0, 0, 0, 0, 0, 23, -20, -30, 21],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -29, 27, 10],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 11],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
241
|
MATH
|
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[16, -8, -4, 12, -13, 7, -3, -20, -2, -4, 19, -4],\n [-8, -34, 6, -26, -24, 4, -7, -12, -6, -6, -14, -14],\n [-4, 6, -14, 15, 24, -17, 9, -4, 0, 16, -2, -3],\n [12, -26, 15, -31, -16, 16, -12, 13, 28, 4, -9, 18],\n [-13, -24, 24, -16, -5, 12, 18, 20, 6, 2, 0, 12],\n [7, 4, -17, 16, 12, -19, -22, -6, 2, 12, 10, -28],\n [-3, -7, 9, -12, 18, -22, 29, 21, 10, 13, -2, -18],\n [-20, -12, -4, 13, 20, -6, 21, -24, 12, -2, 24, 11],\n [-2, -6, 0, 28, 6, 2, 10, 12, -11, -14, 20, -3],\n [-4, -6, 16, 4, 2, 12, 13, -2, -14, -4, 15, -20],\n [19, -14, -2, -9, 0, 10, -2, 24, 20, 15, -12, -18],\n [-4, -14, -3, 18, 12, -28, -18, 11, -3, -20, -18, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
101
|
MATH
|
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[-22, -2, 22, -14, 34, 0, 9, 0, -14, 25, 20, -3],\n [0, 0, -16, -18, 2, 31, -13, -20, 23, 33, 32, -15],\n [0, 0, -20, -22, 25, 35, 10, -4, -21, 8, -19, 5],\n [0, 0, 0, -9, 7, -5, -19, 18, 26, -4, 4, -23],\n [0, 0, 0, 0, -11, -14, 30, 9, 33, -35, 8, 3],\n [0, 0, 0, 0, 0, 10, 31, 29, 22, 17, -35, 30],\n [0, 0, 0, 0, 0, 0, -33, 24, -1, 33, -16, 3],\n [0, 0, 0, 0, 0, 0, 0, 21, 16, 17, 7, 6],\n [0, 0, 0, 0, 0, 0, 0, 0, 15, -24, 19, -25],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 6, 29],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 7],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
193
|
MATH
|
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[9, -13, -8, 21, -10, -11, 18, -7, 0, -22, -1, -6],\n [0, 31, -6, 9, 15, 11, 17, 28, 2, 28, -29, -14],\n [0, 0, 21, -29, 14, 16, -3, -35, 17, 24, -2, -32],\n [0, 0, 0, -32, -35, 35, 14, 25, -1, -28, -12, 0],\n [0, 0, 0, 0, -18, -8, -7, -20, 11, 23, -5, -32],\n [0, 0, 0, 0, 0, 12, 3, -32, -6, -6, -14, 30],\n [0, 0, 0, 0, 0, 0, 22, -30, 34, 8, -12, -17],\n [0, 0, 0, 0, 0, 0, 0, -27, -15, -7, -3, 26],\n [0, 0, 0, 0, 0, 0, 0, 0, 7, 2, 1, 22],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 6, -11, 21],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14, -4],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
206
|
MATH
|
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[-1, -10, -8, -14, 5, 0, -4, -4, 8, -22, 12, 13],\n [-10, -28, -28, 32, -3, 6, 9, -19, 18, 17, -3, -14],\n [-8, -28, -26, 14, 14, -6, 12, 4, 12, -15, -1, 6],\n [-14, 32, 14, -11, 1, 18, -3, 16, -11, -16, 14, 16],\n [5, -3, 14, 1, -9, -14, -18, 28, -5, 30, 2, -8],\n [0, 6, -6, 18, -14, 33, -16, -10, 11, 8, 8, 6],\n [-4, 9, 12, -3, -18, -16, 9, -4, 14, 1, -11, -16],\n [-4, -19, 4, 16, 28, -10, -4, -8, 20, 4, 8, -9],\n [8, 18, 12, -11, -5, 11, 14, 20, 9, -4, 16, -2],\n [-22, 17, -15, -16, 30, 8, 1, 4, -4, -15, -4, 8],\n [12, -3, -1, 14, 2, 8, -11, 8, 16, -4, -27, 5],\n [13, -14, 6, 16, -8, 6, -16, -9, -2, 8, 5, 22]]\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[[5, -1, 10, -9, -9, -27, 3, 10, -2, 0, -22, -15],\n [-1, -1, -4, -16, -10, 8, 7, 6, 8, -21, -6, -15],\n [10, -4, 6, -11, -17, 22, -1, -4, 16, -18, -8, 13],\n [-9, -16, -11, -26, -13, -23, 30, -4, -4, 20, -4, -30],\n [-9, -10, -17, -13, -21, 24, 0, -24, 5, -19, -32, -10],\n [-27, 8, 22, -23, 24, 27, -4, -3, -7, -4, -6, 1],\n [3, 7, -1, 30, 0, -4, 24, -24, 18, 17, -16, 4],\n [10, 6, -4, -4, -24, -3, -24, -11, -22, 8, 0, 17],\n [-2, 8, 16, -4, 5, -7, 18, -22, 19, 13, 6, -18],\n [0, -21, -18, 20, -19, -4, 17, 8, 13, 9, -20, 4],\n [-22, -6, -8, -4, -32, -6, -16, 0, 6, -20, 19, 15],\n [-15, -15, 13, -30, -10, 1, 4, 17, -18, 4, 15, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
89
|
MATH
|
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[15, -22, 18, 11, -16, -8, -20, 24, -8, 29, -7, 0],\n [-22, -9, -33, 24, -8, -14, 4, 14, -9, 12, 10, 18],\n [18, -33, 12, 0, -12, 23, -26, 0, -4, 8, -12, 2],\n [11, 24, 0, -9, -12, 20, 16, 0, -21, 2, 16, 9],\n [-16, -8, -12, -12, 26, 10, 14, 7, -2, 11, 5, -22],\n [-8, -14, 23, 20, 10, -1, -18, 6, 15, -18, 26, -30],\n [-20, 4, -26, 16, 14, -18, 28, 0, 6, 10, 34, 8],\n [24, 14, 0, 0, 7, 6, 0, -7, 0, -6, 8, 18],\n [-8, -9, -4, -21, -2, 15, 6, 0, -8, 11, -2, 24],\n [29, 12, 8, 2, 11, -18, 10, -6, 11, 25, 5, 1],\n [-7, 10, -12, 16, 5, 26, 34, 8, -2, 5, 34, 22],\n [0, 18, 2, 9, -22, -30, 8, 18, 24, 1, 22, 34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
109
|
MATH
|
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[-16, -9, 2, 29, 18, -12, 11, 35, 27, 21, 19, 24],\n [0, -6, -14, -7, 5, 6, 29, -5, -6, -18, -19, 2],\n [0, 0, -14, 31, 20, -17, 21, 8, -1, -35, 16, 34],\n [0, 0, 0, -35, -15, 17, -20, 25, 18, 4, -10, 29],\n [0, 0, 0, 0, -13, -29, 8, 17, 35, -2, 10, 32],\n [0, 0, 0, 0, 0, 14, -24, 34, -14, -4, -35, 18],\n [0, 0, 0, 0, 0, 0, -13, -10, -29, 8, -9, -10],\n [0, 0, 0, 0, 0, 0, 0, 19, 2, -7, -10, -1],\n [0, 0, 0, 0, 0, 0, 0, 0, 22, -4, -5, 7],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -15, 24, 27],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 28, 23],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
35
|
MATH
|
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[2, 4, -6, -3, 0, 23, -25, 8, -8, 18, 8, 21],\n [4, 22, -1, -14, 23, 6, 12, -26, -7, 18, 10, -26],\n [-6, -1, -7, -11, -24, 18, -10, -16, 4, -18, 0, 12],\n [-3, -14, -11, 13, 15, -34, 10, 0, -15, -10, -16, 0],\n [0, 23, -24, 15, 19, 2, 26, -8, 11, 9, -14, 2],\n [23, 6, 18, -34, 2, -11, -14, -22, -6, -18, -6, -10],\n [-25, 12, -10, 10, 26, -14, -10, 8, 6, 30, 14, 2],\n [8, -26, -16, 0, -8, -22, 8, -3, 0, -12, -22, -14],\n [-8, -7, 4, -15, 11, -6, 6, 0, 10, -26, 21, -28],\n [18, 18, -18, -10, 9, -18, 30, -12, -26, -24, 24, 24],\n [8, 10, 0, -16, -14, -6, 14, -22, 21, 24, -25, -20],\n [21, -26, 12, 0, 2, -10, 2, -14, -28, 24, -20, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
553
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-15, -15, -25, 2, -1, -22, -22, -26, -24, 2, -2, 5],\n [0, -19, -19, 31, 26, -35, -24, -32, 6, -23, -32, 33],\n [0, 0, -24, -30, -28, 15, -25, 27, 21, -24, -34, -28],\n [0, 0, 0, -28, 0, -22, 18, -15, 14, 3, -16, -29],\n [0, 0, 0, 0, 2, 25, 8, 8, 26, -30, -19, 15],\n [0, 0, 0, 0, 0, 34, 21, 3, -3, 23, -18, 20],\n [0, 0, 0, 0, 0, 0, -4, -10, -11, -13, 21, 16],\n [0, 0, 0, 0, 0, 0, 0, -3, -1, 15, -18, -6],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 11, -23],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -24, -12, -2],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -33, 22],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
34
|
MATH
|
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-31, 16, 5, 17, 14, -21, -29, 4, -8, -4, -21, 34],\n [0, -32, -25, -10, 25, 1, -13, 4, -13, -20, 25, 32],\n [0, 0, -11, 8, -24, -27, -24, 33, 18, 18, -8, 20],\n [0, 0, 0, 2, 32, 17, -3, 35, 20, 15, 7, -21],\n [0, 0, 0, 0, 15, -26, -24, -32, -18, 0, -11, 0],\n [0, 0, 0, 0, 0, 7, -1, 27, -32, 5, 9, 14],\n [0, 0, 0, 0, 0, 0, -1, 10, 6, 3, 13, 26],\n [0, 0, 0, 0, 0, 0, 0, 35, -34, 13, -5, 4],\n [0, 0, 0, 0, 0, 0, 0, 0, 32, 28, -6, 0],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -13, -8, -20],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, -17],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
228
|
MATH
|
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[-26, -2, 0, 18, 7, 3, -2, -19, 10, -2, -4, 18],\n [-2, 21, 26, 0, -4, 17, 14, -2, 24, -9, 5, 10],\n [0, 26, 7, 16, 3, -22, -2, 27, -30, 13, 6, -21],\n [18, 0, 16, -11, -12, -30, -16, -12, -4, 9, 2, -1],\n [7, -4, 3, -12, 4, 29, -15, 26, 5, 18, 12, 9],\n [3, 17, -22, -30, 29, 6, 20, 8, -14, -3, 2, -10],\n [-2, 14, -2, -16, -15, 20, 3, 34, -16, -18, 6, -6],\n [-19, -2, 27, -12, 26, 8, 34, 15, -8, -24, 26, -12],\n [10, 24, -30, -4, 5, -14, -16, -8, -27, -5, -5, -22],\n [-2, -9, 13, 9, 18, -3, -18, -24, -5, 23, 30, -8],\n [-4, 5, 6, 2, 12, 2, 6, 26, -5, 30, 0, 5],\n [18, 10, -21, -1, 9, -10, -6, -12, -22, -8, 5, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
530
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[-8, 26, -4, 13, 2, 12, -25, 2, -6, 30, 0, -14],\n [26, -24, -16, -10, -12, -3, -1, 4, -22, 14, 11, 14],\n [-4, -16, 34, 12, 28, 7, 14, 6, 7, 9, 24, 12],\n [13, -10, 12, 31, -8, 0, -6, -1, 25, -6, -12, -22],\n [2, -12, 28, -8, -15, -4, -12, 2, -2, -10, -1, 5],\n [12, -3, 7, 0, -4, 32, -2, -24, -6, -20, -9, 6],\n [-25, -1, 14, -6, -12, -2, 19, 4, 28, -1, -6, 20],\n [2, 4, 6, -1, 2, -24, 4, 21, 0, 22, 8, -26],\n [-6, -22, 7, 25, -2, -6, 28, 0, 35, 16, 16, 12],\n [30, 14, 9, -6, -10, -20, -1, 22, 16, -19, -2, -13],\n [0, 11, 24, -12, -1, -9, -6, 8, 16, -2, -31, -13],\n [-14, 14, 12, -22, 5, 6, 20, -26, 12, -13, -13, -34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
543
|
MATH
|
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-23, 5, 23, 33, 17, 9, -16, -12, 25, 22, -9, -10],\n [0, 6, 11, 17, 23, 2, 33, 17, -21, -10, 12, -17],\n [0, 0, 18, 15, 3, -32, -33, 28, -7, -25, 22, -9],\n [0, 0, 0, 30, 0, 29, 27, -1, -5, -8, -35, -11],\n [0, 0, 0, 0, -34, 28, 33, -27, -34, -2, 24, 25],\n [0, 0, 0, 0, 0, 13, -33, -31, 25, -10, -31, -21],\n [0, 0, 0, 0, 0, 0, 11, -23, 19, -15, 30, 18],\n [0, 0, 0, 0, 0, 0, 0, 35, 28, -15, 27, 28],\n [0, 0, 0, 0, 0, 0, 0, 0, -26, -7, 0, 1],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 15, 13, 7],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9, -35],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
254
|
MATH
|
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-14, 1, -16, -12, 29, 29, -35, -33, 10, 19, 28, 9],\n [0, 29, -12, -1, -12, -8, -20, 23, 18, -20, -21, -25],\n [0, 0, 7, 33, -23, -26, 5, 14, 35, 23, 3, -33],\n [0, 0, 0, -3, 12, -34, 35, -4, -32, -16, 0, -4],\n [0, 0, 0, 0, -1, -6, 18, 0, 19, 22, 29, 33],\n [0, 0, 0, 0, 0, 0, 16, 17, 14, 5, -18, -14],\n [0, 0, 0, 0, 0, 0, 18, -19, 24, -5, 13, -34],\n [0, 0, 0, 0, 0, 0, 0, 5, -20, -32, -24, -7],\n [0, 0, 0, 0, 0, 0, 0, 0, -27, 13, -3, -18],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -32, 21, 13],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, 16],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
32
|
MATH
|
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-7, -33, 21, -6, -27, -10, -34, 26, -33, 10, 32, -11],\n [0, -23, 8, -1, 19, -27, -34, 25, 5, 8, 28, -5],\n [0, 0, 33, 22, 8, 20, 7, -2, -6, 35, 34, 19],\n [0, 0, 0, -10, 21, -12, 17, 34, 7, 24, 22, 13],\n [0, 0, 0, 0, 16, 10, 8, -14, 17, 23, -6, -28],\n [0, 0, 0, 0, 0, -9, 4, -10, -9, 26, 14, 6],\n [0, 0, 0, 0, 0, 0, -13, -29, -10, -24, -31, 33],\n [0, 0, 0, 0, 0, 0, 0, -13, -18, -6, -10, -20],\n [0, 0, 0, 0, 0, 0, 0, 0, 10, 14, 2, -18],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 3, -24],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -27, 16],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 28]]\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[[-17, -2, -4, 10, 2, 13, 14, -16, 2, -20, -5, 19],\n [-2, 1, 8, 2, -14, 10, -25, 3, -4, 5, 12, 2],\n [-4, 8, 7, 22, 10, -16, -3, -22, -18, 12, -10, 7],\n [10, 2, 22, -11, 23, 2, 4, -2, -3, 3, 1, -18],\n [2, -14, 10, 23, 8, 12, -12, -12, -4, -18, 28, 2],\n [13, 10, -16, 2, 12, 30, -10, -6, 12, 12, 17, 6],\n [14, -25, -3, 4, -12, -10, 22, 2, 8, -6, -6, 2],\n [-16, 3, -22, -2, -12, -6, 2, 5, 0, -16, 2, -9],\n [2, -4, -18, -3, -4, 12, 8, 0, -14, 16, 12, 8],\n [-20, 5, 12, 3, -18, 12, -6, -16, 16, 11, -5, -19],\n [-5, 12, -10, 1, 28, 17, -6, 2, 12, -5, -29, -24],\n [19, 2, 7, -18, 2, 6, 2, -9, 8, -19, -24, -19]]\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[[-13, 21, 22, -22, -16, -6, -17, 17, 20, -13, 26, -3],\n [0, -3, -4, 25, 18, -19, -17, 34, -2, -11, 32, -25],\n [0, 0, -29, -20, -20, 4, -24, -1, -15, 14, 7, -19],\n [0, 0, 0, -9, -16, -11, 30, -27, 17, 25, 2, -33],\n [0, 0, 0, 0, 9, 11, -10, -22, 18, 35, 10, -5],\n [0, 0, 0, 0, 0, 22, -12, 27, -11, 23, -4, -18],\n [0, 0, 0, 0, 0, 0, -6, 17, 27, -25, -5, 13],\n [0, 0, 0, 0, 0, 0, 0, -10, -34, -21, -32, 14],\n [0, 0, 0, 0, 0, 0, 0, 0, -18, 19, 14, -22],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -11, -15, -26],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -27, -1],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
170
|
MATH
|
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-7, -12, -4, -16, 20, -16, -10, 0, -24, 5, -5, 11],\n [-12, 11, -3, 25, 6, 10, 6, -21, 4, -2, -15, -20],\n [-4, -3, -8, -6, -22, 11, -18, -6, 17, -9, 22, 16],\n [-16, 25, -6, -29, -10, 8, 0, 20, -13, 0, -14, 12],\n [20, 6, -22, -10, 31, -10, -10, -2, 4, -8, -6, -2],\n [-16, 10, 11, 8, -10, -11, -12, -17, 1, -17, 12, 1],\n [-10, 6, -18, 0, -10, -12, -33, 2, 0, 15, -24, -10],\n [0, -21, -6, 20, -2, -17, 2, -35, 7, -12, -4, 31],\n [-24, 4, 17, -13, 4, 1, 0, 7, 18, -4, 21, 5],\n [5, -2, -9, 0, -8, -17, 15, -12, -4, -1, 14, 16],\n [-5, -15, 22, -14, -6, 12, -24, -4, 21, 14, -27, 4],\n [11, -20, 16, 12, -2, 1, -10, 31, 5, 16, 4, -28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
82
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-26, 24, -27, -8, -25, -4, 20, -3, -22, 22, -2, 2],\n [24, 20, -24, 0, -22, 12, -20, 1, -6, 2, 25, 7],\n [-27, -24, 20, -6, 3, 1, -24, 12, 10, 2, 4, -2],\n [-8, 0, -6, -23, -8, -2, 2, 2, -24, 12, -9, 0],\n [-25, -22, 3, -8, -5, 10, -24, -24, 6, -10, 23, 8],\n [-4, 12, 1, -2, 10, -28, -6, -10, 20, -12, -1, 5],\n [20, -20, -24, 2, -24, -6, 2, -14, 0, 5, -2, -1],\n [-3, 1, 12, 2, -24, -10, -14, 7, -16, 10, 18, 8],\n [-22, -6, 10, -24, 6, 20, 0, -16, -13, -13, 21, 16],\n [22, 2, 2, 12, -10, -12, 5, 10, -13, 14, -16, 10],\n [-2, 25, 4, -9, 23, -1, -2, 18, 21, -16, 25, -4],\n [2, 7, -2, 0, 8, 5, -1, 8, 16, 10, -4, 23]]\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[[13, 5, 4, -18, -19, 16, 28, 22, 14, -26, 2, 0],\n [5, 31, -4, 0, 7, 1, -8, 2, 22, -10, 8, -14],\n [4, -4, -26, 35, -2, -21, 24, 0, 0, -16, -16, 5],\n [-18, 0, 35, 35, -7, 2, 0, 12, 29, 16, 0, -18],\n [-19, 7, -2, -7, 35, -12, 8, -14, -5, -32, -14, 26],\n [16, 1, -21, 2, -12, 3, 18, 10, -6, -16, 4, 0],\n [28, -8, 24, 0, 8, 18, 34, -9, 24, -14, 0, 17],\n [22, 2, 0, 12, -14, 10, -9, 29, -15, 0, -22, 1],\n [14, 22, 0, 29, -5, -6, 24, -15, -10, 10, 6, -18],\n [-26, -10, -16, 16, -32, -16, -14, 0, 10, -3, -18, 6],\n [2, 8, -16, 0, -14, 4, 0, -22, 6, -18, 10, -8],\n [0, -14, 5, -18, 26, 0, 17, 1, -18, 6, -8, 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[[-19, 4, 13, 21, 28, 21, 34, 7, -13, -9, 22, 1],\n [0, 29, -30, 14, -14, -11, 15, 12, 34, 29, 24, 10],\n [0, 0, 2, -25, -24, 6, 3, 35, -25, 0, 16, -5],\n [0, 0, 0, 5, 22, 20, -12, -5, 19, -26, 24, -34],\n [0, 0, 0, 0, 34, 31, 20, 27, -21, -26, 2, 11],\n [0, 0, 0, 0, 0, -34, 7, -10, 35, 2, 6, -31],\n [0, 0, 0, 0, 0, 0, 25, -15, 32, -24, -14, -16],\n [0, 0, 0, 0, 0, 0, 0, 24, 19, -12, -12, 18],\n [0, 0, 0, 0, 0, 0, 0, 0, 1, 22, 18, 3],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 6, -4, -4],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14, -2],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
223
|
MATH
|
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[12, -29, 33, -20, -35, 1, 1, 28, 26, 25, -3, 30],\n [0, -16, 24, -12, -32, 1, -32, -18, 30, 12, -3, 22],\n [0, 0, -26, 29, 6, -27, 24, -21, 21, 33, -14, 28],\n [0, 0, 0, -13, -11, -30, -2, 27, -27, 24, 13, 15],\n [0, 0, 0, 0, 5, 26, 22, -22, 0, 0, -28, -10],\n [0, 0, 0, 0, 0, 15, 6, -7, -26, 3, -35, 3],\n [0, 0, 0, 0, 0, 0, -16, -26, -2, 12, -3, 25],\n [0, 0, 0, 0, 0, 0, 0, -13, -19, -23, -22, -25],\n [0, 0, 0, 0, 0, 0, 0, 0, 23, 14, 33, 34],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -11, -33, -27],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, -23],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16]]\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[[-15, 21, 14, -10, -6, -5, 6, 32, 25, 25, 34, 32],\n [0, -17, 15, 34, 27, -6, -11, 35, -10, 20, -14, -17],\n [0, 0, 6, 5, -13, 11, -23, 30, 30, -20, -8, -1],\n [0, 0, 0, 18, 23, 5, 30, 18, 4, -8, 1, 29],\n [0, 0, 0, 0, -22, 2, -24, 9, -19, -1, 30, 5],\n [0, 0, 0, 0, 0, -2, 13, 18, -5, 22, 6, 22],\n [0, 0, 0, 0, 0, 0, 31, -19, -22, -27, 26, -15],\n [0, 0, 0, 0, 0, 0, 0, -28, -32, -9, 8, 4],\n [0, 0, 0, 0, 0, 0, 0, 0, -10, 3, 22, -17],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -12, -6, 26],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23, 13],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 35]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
219
|
MATH
|
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-21, -2, 26, 16, 5, 5, -5, 8, 0, 13, 25, 2],\n [-2, -16, -12, -10, -12, 25, -22, -3, 6, -25, 6, 8],\n [26, -12, 29, -22, -23, 0, -11, 14, 2, -19, 20, 10],\n [16, -10, -22, 35, 4, 3, -16, -1, 8, -7, 16, 14],\n [5, -12, -23, 4, -20, -6, -20, 9, -14, -3, 12, 16],\n [5, 25, 0, 3, -6, -27, -24, 8, 8, 2, -8, 12],\n [-5, -22, -11, -16, -20, -24, 26, -20, -4, -22, 3, 7],\n [8, -3, 14, -1, 9, 8, -20, -35, -16, 7, 8, -25],\n [0, 6, 2, 8, -14, 8, -4, -16, -35, 4, -16, 10],\n [13, -25, -19, -7, -3, 2, -22, 7, 4, 32, -24, 0],\n [25, 6, 20, 16, 12, -8, 3, 8, -16, -24, 23, 3],\n [2, 8, 10, 14, 16, 12, 7, -25, 10, 0, 3, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
565
|
MATH
|
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[2, 34, 17, 8, 18, -16, -5, -29, 22, -26, -26, 3],\n [0, -6, 1, 31, 7, 16, 20, 32, -27, -13, 27, 25],\n [0, 0, -12, 15, 22, -3, -20, -14, 21, 26, 35, 34],\n [0, 0, 0, 21, -27, -5, 35, -27, -23, 22, -33, -1],\n [0, 0, 0, 0, -1, -21, -30, -4, 16, -8, 28, -17],\n [0, 0, 0, 0, 0, 17, 20, 23, 34, 22, -23, 7],\n [0, 0, 0, 0, 0, 0, -8, -7, -19, 32, 8, 25],\n [0, 0, 0, 0, 0, 0, 0, -9, -18, 18, -35, 25],\n [0, 0, 0, 0, 0, 0, 0, 0, 20, 11, -26, 13],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -30, 2, 5],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, -18],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -21]]\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[[-34, -10, 31, 32, -12, 10, -3, 8, 1, -8, 12, -32],\n [-10, -35, -10, 5, 6, 1, 7, -6, -16, -24, -14, -18],\n [31, -10, 34, 13, 9, 17, -12, 9, 10, 16, 9, -10],\n [32, 5, 13, 12, -4, -22, 22, -1, -4, 12, 8, 6],\n [-12, 6, 9, -4, 5, 12, 1, 14, 20, 4, -4, 5],\n [10, 1, 17, -22, 12, -11, -6, 14, -26, 4, -12, 5],\n [-3, 7, -12, 22, 1, -6, 0, 20, 3, 15, 5, 3],\n [8, -6, 9, -1, 14, 14, 20, 1, -6, 16, -7, 12],\n [1, -16, 10, -4, 20, -26, 3, -6, 15, 0, 8, 7],\n [-8, -24, 16, 12, 4, 4, 15, 16, 0, -29, -16, 22],\n [12, -14, 9, 8, -4, -12, 5, -7, 8, -16, 10, 4],\n [-32, -18, -10, 6, 5, 5, 3, 12, 7, 22, 4, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
505
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[1, 30, -19, 4, 2, 25, -27, 25, -20, -34, 7, 6],\n [0, 31, -6, -23, -17, -29, -27, 18, 25, -34, 14, -5],\n [0, 0, -3, -29, -5, 12, 11, 17, -17, -30, 13, 14],\n [0, 0, 0, 33, 23, 0, -33, 22, 19, 21, -19, 3],\n [0, 0, 0, 0, -15, -15, 16, 7, 16, 31, 8, -4],\n [0, 0, 0, 0, 0, 17, 15, 17, -32, -19, 31, 11],\n [0, 0, 0, 0, 0, 0, 22, 23, -35, -33, 31, 1],\n [0, 0, 0, 0, 0, 0, 0, 12, -33, -13, 32, -15],\n [0, 0, 0, 0, 0, 0, 0, 0, 29, 25, -17, 10],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, -3, -3],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23, 16],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
214
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-13, -4, 4, -15, 13, 18, -26, 30, -2, -25, -2, 6],\n [-4, 33, 6, -16, -31, -2, -11, 22, 2, 5, -17, -2],\n [4, 6, 26, -20, -2, -26, 12, 0, -9, 22, 0, -20],\n [-15, -16, -20, 35, -24, -8, 16, -4, -16, 7, 4, -8],\n [13, -31, -2, -24, -17, -12, 18, 2, 7, -4, 8, -14],\n [18, -2, -26, -8, -12, 9, -4, 8, 16, -16, 0, 24],\n [-26, -11, 12, 16, 18, -4, -17, 2, -28, -18, -28, 2],\n [30, 22, 0, -4, 2, 8, 2, -15, -22, -19, -5, 6],\n [-2, 2, -9, -16, 7, 16, -28, -22, 5, 26, -2, -4],\n [-25, 5, 22, 7, -4, -16, -18, -19, 26, 19, 0, -5],\n [-2, -17, 0, 4, 8, 0, -28, -5, -2, 0, 2, -4],\n [6, -2, -20, -8, -14, 24, 2, 6, -4, -5, -4, -33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
83
|
MATH
|
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-3, 24, 22, -28, 10, -14, -9, 16, -27, -4, 12, 16],\n [24, -22, 22, 10, 12, 9, -2, 14, -11, 6, 0, 10],\n [22, 22, 16, 0, 2, 0, -14, 20, 12, -26, -9, 1],\n [-28, 10, 0, -6, -28, -5, 14, -12, -17, -16, 0, 8],\n [10, 12, 2, -28, -5, 8, -31, -24, -2, 32, 32, 12],\n [-14, 9, 0, -5, 8, 4, 4, -8, -6, -5, -6, 8],\n [-9, -2, -14, 14, -31, 4, 32, 22, 10, -24, -1, 21],\n [16, 14, 20, -12, -24, -8, 22, 30, 18, 4, 22, -18],\n [-27, -11, 12, -17, -2, -6, 10, 18, 19, -2, 10, 29],\n [-4, 6, -26, -16, 32, -5, -24, 4, -2, -12, 18, 0],\n [12, 0, -9, 0, 32, -6, -1, 22, 10, 18, 0, -8],\n [16, 10, 1, 8, 12, 8, 21, -18, 29, 0, -8, -23]]\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[[7, 24, 21, 35, -19, 14, -4, -14, 19, 21, -23, 11],\n [0, 18, -7, -14, 29, -7, 12, -31, -1, 35, 10, -1],\n [0, 0, -26, 30, 34, -11, 8, 24, 11, 4, -29, 10],\n [0, 0, 0, -15, -35, -17, 24, -3, -32, -33, 16, -8],\n [0, 0, 0, 0, -20, -12, 33, 5, 11, 33, -5, -6],\n [0, 0, 0, 0, 0, -18, 20, -5, 23, -34, 3, 25],\n [0, 0, 0, 0, 0, 0, -1, -25, 25, 8, 32, -11],\n [0, 0, 0, 0, 0, 0, 0, -33, 26, 28, -19, 26],\n [0, 0, 0, 0, 0, 0, 0, 0, -20, -18, -29, 9],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 19, 20, 8],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -33],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
33
|
MATH
|
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-20, -10, -4, -4, 12, 8, 17, -9, -18, -8, -10, -9],\n [-10, 15, -5, 20, 32, 4, 9, 5, -13, -16, 3, -26],\n [-4, -5, -35, -11, -10, -14, 18, 18, -14, -10, -18, -4],\n [-4, 20, -11, -9, -4, -14, 34, -6, 12, -3, -14, -4],\n [12, 32, -10, -4, -26, -8, -4, 4, -22, -7, -2, 12],\n [8, 4, -14, -14, -8, 0, -7, -31, -16, 8, -6, 0],\n [17, 9, 18, 34, -4, -7, 32, 8, -2, 12, 5, -6],\n [-9, 5, 18, -6, 4, -31, 8, -29, 6, 18, 15, 4],\n [-18, -13, -14, 12, -22, -16, -2, 6, 25, -8, -22, -11],\n [-8, -16, -10, -3, -7, 8, 12, 18, -8, 15, -1, -12],\n [-10, 3, -18, -14, -2, -6, 5, 15, -22, -1, -5, -21],\n [-9, -26, -4, -4, 12, 0, -6, 4, -11, -12, -21, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
86
|
MATH
|
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-16, -16, 8, 21, -16, 2, 10, 34, -21, 8, -23, -32],\n [-16, -9, 2, -30, -3, 18, -1, -18, 4, 12, 24, 22],\n [8, 2, -11, 12, -12, 24, -17, 24, -16, 4, 33, 0],\n [21, -30, 12, -13, 6, -2, -32, 20, -16, 14, 2, 22],\n [-16, -3, -12, 6, -2, 10, 3, 22, 4, 15, 4, -2],\n [2, 18, 24, -2, 10, -27, 12, -11, 15, 15, 12, 30],\n [10, -1, -17, -32, 3, 12, 27, 4, 2, -24, 3, 8],\n [34, -18, 24, 20, 22, -11, 4, 18, -6, -14, 6, 24],\n [-21, 4, -16, -16, 4, 15, 2, -6, -13, -28, 9, 23],\n [8, 12, 4, 14, 15, 15, -24, -14, -28, 26, 4, -8],\n [-23, 24, 33, 2, 4, 12, 3, 6, 9, 4, -30, 19],\n [-32, 22, 0, 22, -2, 30, 8, 24, 23, -8, 19, -4]]\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[[15, 17, 10, -2, 14, 2, -7, 20, 24, 0, 13, 12],\n [17, 19, -24, 30, 10, 2, 28, -12, -20, -9, -22, 27],\n [10, -24, -35, -24, -5, -20, 16, 27, 27, -22, 20, -3],\n [-2, 30, -24, 25, -28, 8, 21, 15, 0, 7, -2, 30],\n [14, 10, -5, -28, -1, -1, -10, 9, -22, 12, -6, 10],\n [2, 2, -20, 8, -1, -7, -26, 2, 22, 9, -1, -2],\n [-7, 28, 16, 21, -10, -26, -1, 6, -2, -10, 0, -5],\n [20, -12, 27, 15, 9, 2, 6, 26, -16, -3, 16, -16],\n [24, -20, 27, 0, -22, 22, -2, -16, 1, -14, 11, -14],\n [0, -9, -22, 7, 12, 9, -10, -3, -14, -19, 16, -16],\n [13, -22, 20, -2, -6, -1, 0, 16, 11, 16, 3, -4],\n [12, 27, -3, 30, 10, -2, -5, -16, -14, -16, -4, -27]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
100
|
MATH
|
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-29, -20, -17, -30, -25, 25, 6, -23, -24, -16, 14, 0],\n [0, 1, -24, 4, 18, -34, 14, 5, 9, -27, 26, 11],\n [0, 0, 8, -14, 2, -17, -5, 31, 6, -10, -23, 22],\n [0, 0, 0, 19, 22, 27, 16, -12, -27, 1, 17, -12],\n [0, 0, 0, 0, 33, -22, 6, 14, 25, -32, -19, 21],\n [0, 0, 0, 0, 0, 11, -30, 35, -2, 17, -22, -20],\n [0, 0, 0, 0, 0, 0, -7, 34, 23, 28, -12, -20],\n [0, 0, 0, 0, 0, 0, 0, 35, 15, 29, 16, -6],\n [0, 0, 0, 0, 0, 0, 0, 0, 9, -24, 13, -5],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -27, 0, 4],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -30, -29],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
225
|
MATH
|
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[-28, 5, -33, 33, -22, -10, 34, 22, 4, 15, -31, -4],\n [0, 18, -25, 17, -28, -11, 4, -4, -8, -33, 26, -9],\n [0, 0, 25, 8, 10, -22, -28, 12, -22, 29, -29, 13],\n [0, 0, 0, 20, -21, 21, 22, -1, -20, -28, 9, 4],\n [0, 0, 0, 0, -9, 11, -30, 19, 8, -18, -20, -24],\n [0, 0, 0, 0, 0, 11, -7, 9, -27, -12, -21, 0],\n [0, 0, 0, 0, 0, 0, -9, -35, -2, 32, -15, -3],\n [0, 0, 0, 0, 0, 0, 0, -7, -19, 24, -14, -12],\n [0, 0, 0, 0, 0, 0, 0, 0, 12, 21, -15, -16],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -32, -15, -5],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11, 25],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
32
|
MATH
|
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[-21, 18, -22, -16, -12, 4, 16, -12, 2, -27, 14, 1],\n [18, 32, 12, 4, 4, -3, 0, 7, 3, -8, -10, 12],\n [-22, 12, -31, -14, -32, -22, 21, -18, 8, 14, 16, -28],\n [-16, 4, -14, 13, -26, 22, 18, -2, -8, 17, -16, -8],\n [-12, 4, -32, -26, -5, 2, 20, -13, -1, 20, -30, 6],\n [4, -3, -22, 22, 2, -10, -24, 9, -12, 32, 7, -10],\n [16, 0, 21, 18, 20, -24, -34, 22, -9, -4, -22, -8],\n [-12, 7, -18, -2, -13, 9, 22, -33, 6, 20, -1, -12],\n [2, 3, 8, -8, -1, -12, -9, 6, -26, -22, 2, -12],\n [-27, -8, 14, 17, 20, 32, -4, 20, -22, -15, -13, 9],\n [14, -10, 16, -16, -30, 7, -22, -1, 2, -13, -30, -12],\n [1, 12, -28, -8, 6, -10, -8, -12, -12, 9, -12, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
551
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-26, -3, -23, 20, -2, 30, -32, 6, -8, 6, -8, 4],\n [-3, -16, -10, 4, -15, -2, 2, 0, 2, -8, -12, -24],\n [-23, -10, -2, 18, 0, 20, 2, -2, -12, 24, 23, 2],\n [20, 4, 18, 4, 16, 2, 0, -2, -14, -10, -14, -25],\n [-2, -15, 0, 16, -24, -10, 6, 8, -6, -4, -19, 0],\n [30, -2, 20, 2, -10, 7, 2, -17, 4, -2, 4, -6],\n [-32, 2, 2, 0, 6, 2, 33, 22, -8, -28, 12, -1],\n [6, 0, -2, -2, 8, -17, 22, 3, -4, -4, 8, 4],\n [-8, 2, -12, -14, -6, 4, -8, -4, 11, 25, -6, -20],\n [6, -8, 24, -10, -4, -2, -28, -4, 25, 16, -15, -2],\n [-8, -12, 23, -14, -19, 4, 12, 8, -6, -15, -19, -18],\n [4, -24, 2, -25, 0, -6, -1, 4, -20, -2, -18, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
83
|
MATH
|
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[4, -2, 9, 35, 35, -9, 8, -3, -3, 8, -16, 0],\n [0, -4, 31, 3, -12, 34, 18, 2, -4, 9, 25, 34],\n [0, 0, 20, -9, 2, 26, -18, 28, -6, 13, 5, -23],\n [0, 0, 0, -18, -31, -17, 6, -18, -4, -15, -26, 1],\n [0, 0, 0, 0, -27, 8, 10, -28, 1, -17, 27, 10],\n [0, 0, 0, 0, 0, 27, -33, -8, -7, -18, -1, 11],\n [0, 0, 0, 0, 0, 0, 26, -20, 8, 22, -30, -21],\n [0, 0, 0, 0, 0, 0, 0, -27, 27, -3, -15, 19],\n [0, 0, 0, 0, 0, 0, 0, 0, -28, -24, 5, -10],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -17, 8, 23],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -23, -30],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
231
|
MATH
|
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[-14, 2, 11, -3, -8, -16, 6, -3, 20, 0, -6, -9],\n [2, 32, 19, -18, 10, 24, 1, 22, -12, -10, 3, 10],\n [11, 19, -21, 2, -1, -12, -23, -16, -26, -28, -14, 20],\n [-3, -18, 2, 15, 18, -1, -16, 17, -30, 12, -2, 2],\n [-8, 10, -1, 18, 17, 2, -11, -4, -5, 20, -6, 18],\n [-16, 24, -12, -1, 2, 33, 6, -2, 25, -22, 2, -18],\n [6, 1, -23, -16, -11, 6, -17, 2, 13, -2, 16, 30],\n [-3, 22, -16, 17, -4, -2, 2, -10, -22, -14, 14, -9],\n [20, -12, -26, -30, -5, 25, 13, -22, -15, -21, -20, 12],\n [0, -10, -28, 12, 20, -22, -2, -14, -21, -26, 14, 10],\n [-6, 3, -14, -2, -6, 2, 16, 14, -20, 14, 28, 17],\n [-9, 10, 20, 2, 18, -18, 30, -9, 12, 10, 17, 28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
553
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-12, 35, -2, 12, -24, -13, -23, 9, 29, 11, 22, -31],\n [0, 24, -15, -12, -18, -15, 18, -26, -12, 24, 21, -13],\n [0, 0, -2, 34, -8, 3, 6, -13, 34, -34, -12, -19],\n [0, 0, 0, 24, 14, -24, 11, 31, 29, -9, 12, 26],\n [0, 0, 0, 0, 19, 11, -34, 3, 9, -4, 29, 2],\n [0, 0, 0, 0, 0, -19, 32, -31, 24, -13, 10, 16],\n [0, 0, 0, 0, 0, 0, 12, -7, -9, -18, 24, 33],\n [0, 0, 0, 0, 0, 0, 0, -2, 6, -16, 32, 9],\n [0, 0, 0, 0, 0, 0, 0, 0, -17, 4, -19, 24],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -16, -33, 1],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, -2],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -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[[-30, -21, 5, 1, 11, -3, 11, 12, -10, 16, -4, -28],\n [-21, 31, -6, -4, 18, -16, -12, -16, 20, -10, 7, -6],\n [5, -6, 18, 21, -2, 28, 10, 26, 6, 20, -14, 6],\n [1, -4, 21, -24, -6, -5, -33, -31, -17, 10, 21, 24],\n [11, 18, -2, -6, -25, -12, -20, -22, 0, 22, -16, -14],\n [-3, -16, 28, -5, -12, -22, 2, 3, -7, 21, -10, 10],\n [11, -12, 10, -33, -20, 2, -25, 16, -32, 22, 4, -1],\n [12, -16, 26, -31, -22, 3, 16, -32, 10, -11, -14, 30],\n [-10, 20, 6, -17, 0, -7, -32, 10, 20, 3, 4, -9],\n [16, -10, 20, 10, 22, 21, 22, -11, 3, -3, -2, 4],\n [-4, 7, -14, 21, -16, -10, 4, -14, 4, -2, 2, -8],\n [-28, -6, 6, 24, -14, 10, -1, 30, -9, 4, -8, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
561
|
MATH
|
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[16, -10, 2, 11, -14, -14, 34, -8, 18, 6, 12, 14],\n [-10, 7, -17, 19, -22, -2, 34, -14, 9, -12, -24, 16],\n [2, -17, -33, 17, -2, -22, -4, -8, -4, 18, 8, -32],\n [11, 19, 17, 24, 24, -19, 2, -10, -12, 13, -14, -6],\n [-14, -22, -2, 24, 14, 18, -24, 4, -6, 4, 14, 16],\n [-14, -2, -22, -19, 18, 15, 31, 20, 2, -7, 5, 20],\n [34, 34, -4, 2, -24, 31, 17, 8, -16, -2, -6, -13],\n [-8, -14, -8, -10, 4, 20, 8, -26, -10, -10, 19, -2],\n [18, 9, -4, -12, -6, 2, -16, -10, -34, -16, -6, 10],\n [6, -12, 18, 13, 4, -7, -2, -10, -16, 24, 16, 0],\n [12, -24, 8, -14, 14, 5, -6, 19, -6, 16, 1, 4],\n [14, 16, -32, -6, 16, 20, -13, -2, 10, 0, 4, -10]]\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[[17, -14, 12, 14, -6, 4, -4, -6, -2, 26, -16, 4],\n [-14, -15, -18, -16, -6, 9, 20, -20, 22, 0, -26, -20],\n [12, -18, 33, -2, -18, -19, 18, -4, 28, -24, -22, 22],\n [14, -16, -2, 11, 32, -6, -26, 16, 0, 16, 30, -6],\n [-6, -6, -18, 32, 9, -14, 13, 17, 19, -20, 0, -18],\n [4, 9, -19, -6, -14, -21, -8, 6, 18, 30, -1, -10],\n [-4, 20, 18, -26, 13, -8, 26, 0, 16, -10, 16, 0],\n [-6, -20, -4, 16, 17, 6, 0, 16, 10, 2, 20, 4],\n [-2, 22, 28, 0, 19, 18, 16, 10, -31, -14, 3, 2],\n [26, 0, -24, 16, -20, 30, -10, 2, -14, 14, 0, -27],\n [-16, -26, -22, 30, 0, -1, 16, 20, 3, 0, -35, -2],\n [4, -20, 22, -6, -18, -10, 0, 4, 2, -27, -2, 26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
567
|
MATH
|
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-30, 30, -4, 0, -3, 26, 2, -4, 8, -2, -22, -14],\n [30, 4, -16, -14, -14, 8, 15, -20, -12, -16, 22, 9],\n [-4, -16, 25, 17, -32, 12, -1, -6, -8, -3, -30, 6],\n [0, -14, 17, -2, 11, 28, 5, 1, -3, 19, -25, 22],\n [-3, -14, -32, 11, -1, 8, -18, -7, 20, -4, -14, 14],\n [26, 8, 12, 28, 8, -33, -14, -3, 6, 14, -1, 2],\n [2, 15, -1, 5, -18, -14, 30, -2, -2, -10, -26, -9],\n [-4, -20, -6, 1, -7, -3, -2, 17, 14, 4, 30, -16],\n [8, -12, -8, -3, 20, 6, -2, 14, 34, -21, -19, -32],\n [-2, -16, -3, 19, -4, 14, -10, 4, -21, -22, -2, -4],\n [-22, 22, -30, -25, -14, -1, -26, 30, -19, -2, 14, -18],\n [-14, 9, 6, 22, 14, 2, -9, -16, -32, -4, -18, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
92
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-22, 12, -18, -2, -4, -21, -3, -18, 8, -26, -9, -19],\n [12, 0, 2, -22, -8, 6, -20, -4, 8, -27, 6, 25],\n [-18, 2, -20, 13, 4, -27, 31, 10, 25, 1, -17, -24],\n [-2, -22, 13, 32, 20, 28, 0, 12, -8, 21, -3, -23],\n [-4, -8, 4, 20, 26, -30, -8, -28, -29, 19, 19, -25],\n [-21, 6, -27, 28, -30, -28, -2, -24, 22, -8, -8, 14],\n [-3, -20, 31, 0, -8, -2, 1, -10, -14, 0, 3, -3],\n [-18, -4, 10, 12, -28, -24, -10, 9, 30, -6, 8, 0],\n [8, 8, 25, -8, -29, 22, -14, 30, -12, -16, 6, -8],\n [-26, -27, 1, 21, 19, -8, 0, -6, -16, 35, 9, 23],\n [-9, 6, -17, -3, 19, -8, 3, 8, 6, 9, -34, 21],\n [-19, 25, -24, -23, -25, 14, -3, 0, -8, 23, 21, 10]]\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[[16, 14, 14, 14, -2, -3, 8, -15, -8, 26, 8, 10],\n [14, -15, 0, 0, 27, 4, -14, -4, -10, 0, -6, 5],\n [14, 0, -18, 16, -8, 6, 12, -23, 16, -6, 22, 0],\n [14, 0, 16, 4, 3, -1, 8, 4, 2, 13, 2, 24],\n [-2, 27, -8, 3, -8, 6, -17, 17, -16, -22, -19, -17],\n [-3, 4, 6, -1, 6, 31, 1, 6, 0, 8, 25, -17],\n [8, -14, 12, 8, -17, 1, -21, 6, -8, 10, 4, 12],\n [-15, -4, -23, 4, 17, 6, 6, -3, -13, -1, 13, 14],\n [-8, -10, 16, 2, -16, 0, -8, -13, -16, 5, 4, 8],\n [26, 0, -6, 13, -22, 8, 10, -1, 5, 25, -10, 0],\n [8, -6, 22, 2, -19, 25, 4, 13, 4, -10, 30, 12],\n [10, 5, 0, 24, -17, -17, 12, 14, 8, 0, 12, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
80
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-17, 32, -12, 3, 18, 3, -19, -17, 12, -1, -4, 11],\n [0, 28, 10, -1, -19, 6, -7, 34, -19, -22, -12, 21],\n [0, 0, 25, 3, 19, 0, 1, -22, -9, -5, 8, 32],\n [0, 0, 0, -32, 10, 23, -2, -25, -5, -25, 20, 2],\n [0, 0, 0, 0, -28, 24, -2, -20, -23, -14, -9, 28],\n [0, 0, 0, 0, 0, 2, 25, 29, 31, 10, 7, 23],\n [0, 0, 0, 0, 0, 0, -31, 19, -16, -12, 0, -2],\n [0, 0, 0, 0, 0, 0, 0, 14, 9, -23, -20, -23],\n [0, 0, 0, 0, 0, 0, 0, 0, -22, -32, 19, -2],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -22, 18, -30],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 27, -19],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 31]]\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[[-2, -9, 22, 14, 0, -20, 1, 3, -16, 24, 8, -10],\n [-9, 4, 10, -31, 18, 10, -17, 0, 30, 26, -3, 22],\n [22, 10, 20, 12, -5, -26, 26, -18, -9, 12, -4, -14],\n [14, -31, 12, 33, -5, -4, 9, 0, 18, -6, -8, -10],\n [0, 18, -5, -5, 3, -22, 16, 17, 10, 16, -10, -4],\n [-20, 10, -26, -4, -22, 12, 2, 6, 16, -24, -2, -1],\n [1, -17, 26, 9, 16, 2, -21, 14, 13, 8, 6, 27],\n [3, 0, -18, 0, 17, 6, 14, 11, -8, 15, -26, -4],\n [-16, 30, -9, 18, 10, 16, 13, -8, -13, 12, 4, 8],\n [24, 26, 12, -6, 16, -24, 8, 15, 12, -29, -2, 4],\n [8, -3, -4, -8, -10, -2, 6, -26, 4, -2, 14, 29],\n [-10, 22, -14, -10, -4, -1, 27, -4, 8, 4, 29, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
86
|
MATH
|
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-9, -19, -8, 13, -2, 15, 8, -5, -13, -6, 1, -14],\n [-19, -23, 20, 26, -8, 12, 27, -12, -26, 11, 6, -10],\n [-8, 20, -20, -11, 31, -12, 30, -14, 26, -1, 15, -6],\n [13, 26, -11, -9, -19, -14, 9, -9, -29, 14, 4, -6],\n [-2, -8, 31, -19, -13, -7, 16, -19, -8, -4, -18, -14],\n [15, 12, -12, -14, -7, -14, -10, -2, -16, -6, -1, -4],\n [8, 27, 30, 9, 16, -10, -23, -4, -30, 20, 23, 10],\n [-5, -12, -14, -9, -19, -2, -4, 13, 1, 2, 10, -15],\n [-13, -26, 26, -29, -8, -16, -30, 1, 14, -22, -13, 8],\n [-6, 11, -1, 14, -4, -6, 20, 2, -22, -5, 16, 12],\n [1, 6, 15, 4, -18, -1, 23, 10, -13, 16, 2, 17],\n [-14, -10, -6, -6, -14, -4, 10, -15, 8, 12, 17, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
507
|
MATH
|
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-15, -27, -6, -7, -20, -12, 0, -16, 2, -4, -24, -14],\n [-27, -34, -17, 2, -18, -12, -4, -6, 13, 19, 12, -12],\n [-6, -17, 15, 8, -12, 10, 1, 6, 11, 17, -16, 1],\n [-7, 2, 8, 5, 6, -4, 16, 10, -17, 5, 1, -27],\n [-20, -18, -12, 6, -30, -6, 14, -10, 10, 11, 15, -13],\n [-12, -12, 10, -4, -6, -25, -14, -13, -9, 4, 28, 6],\n [0, -4, 1, 16, 14, -14, 23, -8, 19, -6, 6, 10],\n [-16, -6, 6, 10, -10, -13, -8, 3, -30, 18, -18, -4],\n [2, 13, 11, -17, 10, -9, 19, -30, 19, -6, 20, 3],\n [-4, 19, 17, 5, 11, 4, -6, 18, -6, -17, -2, 19],\n [-24, 12, -16, 1, 15, 28, 6, -18, 20, -2, -23, 11],\n [-14, -12, 1, -27, -13, 6, 10, -4, 3, 19, 11, 18]]\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[[21, -5, -3, 10, 14, 12, 12, 4, -14, 17, 12, 5],\n [-5, 29, 12, 0, -26, 12, -18, 10, 3, -19, 6, -2],\n [-3, 12, 2, 7, -4, 2, -30, 16, -8, -14, 10, 22],\n [10, 0, 7, 16, 8, 11, 6, -4, -8, 22, 6, 8],\n [14, -26, -4, 8, -33, 12, -14, 0, -10, 6, -20, 13],\n [12, 12, 2, 11, 12, 14, -18, 19, 15, -20, 7, 18],\n [12, -18, -30, 6, -14, -18, -4, 12, -10, 12, -4, -16],\n [4, 10, 16, -4, 0, 19, 12, -3, -11, 18, -18, -18],\n [-14, 3, -8, -8, -10, 15, -10, -11, 32, 12, 5, 27],\n [17, -19, -14, 22, 6, -20, 12, 18, 12, -27, 28, 8],\n [12, 6, 10, 6, -20, 7, -4, -18, 5, 28, -17, -28],\n [5, -2, 22, 8, 13, 18, -16, -18, 27, 8, -28, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
98
|
MATH
|
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-29, -12, 16, -17, 14, -9, 2, -18, 29, -27, -2, -14],\n [-12, 5, -8, -8, -11, 19, -9, -18, 2, -26, 9, -10],\n [16, -8, 14, 2, 30, -10, 2, -8, -5, 6, -6, -11],\n [-17, -8, 2, -34, 0, 30, 13, -8, -8, 21, 6, 26],\n [14, -11, 30, 0, 3, 14, -31, 24, 7, 22, 6, 4],\n [-9, 19, -10, 30, 14, -34, -2, -16, 2, 18, -8, 18],\n [2, -9, 2, 13, -31, -2, -19, 28, 15, -6, 25, 7],\n [-18, -18, -8, -8, 24, -16, 28, -22, 9, -22, 0, 20],\n [29, 2, -5, -8, 7, 2, 15, 9, -3, 4, 10, -5],\n [-27, -26, 6, 21, 22, 18, -6, -22, 4, 16, -6, 14],\n [-2, 9, -6, 6, 6, -8, 25, 0, 10, -6, -7, 19],\n [-14, -10, -11, 26, 4, 18, 7, 20, -5, 14, 19, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
543
|
MATH
|
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-17, 2, -2, 17, 15, -10, -25, 4, -8, 8, -10, -8],\n [2, -21, -24, 14, -22, -8, -10, -8, 4, 12, 13, -16],\n [-2, -24, -11, -14, -8, 11, -12, -24, -21, 16, 22, 30],\n [17, 14, -14, 29, 14, 2, 6, 6, 1, -18, -1, 0],\n [15, -22, -8, 14, -5, -12, 17, 20, 7, -8, -6, -8],\n [-10, -8, 11, 2, -12, 19, 16, -18, -30, -24, -2, 33],\n [-25, -10, -12, 6, 17, 16, 23, -6, -12, 15, -18, -22],\n [4, -8, -24, 6, 20, -18, -6, -27, -8, -14, -10, -26],\n [-8, 4, -21, 1, 7, -30, -12, -8, -34, -10, -1, -12],\n [8, 12, 16, -18, -8, -24, 15, -14, -10, 0, -2, 22],\n [-10, 13, 22, -1, -6, -2, -18, -10, -1, -2, 22, -8],\n [-8, -16, 30, 0, -8, 33, -22, -26, -12, 22, -8, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
565
|
MATH
|
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[8, 6, 4, 6, 30, -3, 8, 26, -7, -8, 9, -2],\n [6, -17, 27, 0, -22, -11, -2, 6, -5, -5, -30, 14],\n [4, 27, -23, -28, 14, 1, -14, -2, 18, 2, 14, -4],\n [6, 0, -28, -6, 8, -20, 4, 14, 16, 10, 4, -4],\n [30, -22, 14, 8, -4, 1, 0, -14, -14, 15, 18, -4],\n [-3, -11, 1, -20, 1, -25, 10, 9, -18, -18, 10, -8],\n [8, -2, -14, 4, 0, 10, -2, 11, 5, -30, -21, 2],\n [26, 6, -2, 14, -14, 9, 11, -14, 16, -14, 24, -12],\n [-7, -5, 18, 16, -14, -18, 5, 16, 4, 0, -3, 3],\n [-8, -5, 2, 10, 15, -18, -30, -14, 0, -29, -27, -6],\n [9, -30, 14, 4, 18, 10, -21, 24, -3, -27, -18, 2],\n [-2, 14, -4, -4, -4, -8, 2, -12, 3, -6, 2, -32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
517
|
MATH
|
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[31, 10, -4, 0, 9, 10, 0, 2, 7, -2, 24, 7],\n [10, -10, 16, -12, 2, -11, -12, 17, -16, 16, -12, -9],\n [-4, 16, -2, -5, -5, -13, 10, 6, -18, 2, 19, 8],\n [0, -12, -5, 4, 0, 16, -12, 4, 24, -17, -12, -24],\n [9, 2, -5, 0, -4, -10, 2, 20, 2, -18, 0, 9],\n [10, -11, -13, 16, -10, 27, -12, -22, 4, 18, -30, -6],\n [0, -12, 10, -12, 2, -12, 10, -16, 31, -18, 10, -17],\n [2, 17, 6, 4, 20, -22, -16, -30, 27, 10, -2, -3],\n [7, -16, -18, 24, 2, 4, 31, 27, -24, 18, -11, -2],\n [-2, 16, 2, -17, -18, 18, -18, 10, 18, -15, -30, 21],\n [24, -12, 19, -12, 0, -30, 10, -2, -11, -30, 27, -9],\n [7, -9, 8, -24, 9, -6, -17, -3, -2, 21, -9, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
91
|
MATH
|
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[-14, -15, -7, -22, -28, -3, 12, 11, 20, -12, -2, 26],\n [-15, -7, 16, 10, 17, 22, 4, -11, 12, 3, -28, 18],\n [-7, 16, -21, 0, 15, -16, -4, -16, 2, -5, -4, 4],\n [-22, 10, 0, 12, -18, 28, 5, 22, 10, -24, -14, -5],\n [-28, 17, 15, -18, 14, 4, -4, 2, 12, -2, 14, -12],\n [-3, 22, -16, 28, 4, -8, -4, 14, 16, -7, -11, -4],\n [12, 4, -4, 5, -4, -4, -15, -2, -10, 0, -24, 14],\n [11, -11, -16, 22, 2, 14, -2, -7, -22, -1, -22, -5],\n [20, 12, 2, 10, 12, 16, -10, -22, 31, 20, -4, -24],\n [-12, 3, -5, -24, -2, -7, 0, -1, 20, 3, 27, 1],\n [-2, -28, -4, -14, 14, -11, -24, -22, -4, 27, -6, 18],\n [26, 18, 4, -5, -12, -4, 14, -5, -24, 1, 18, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
84
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[9, -1, -8, -29, 26, 15, 10, -16, 2, 25, -4, -10],\n [0, 3, -16, 14, 16, -14, 17, 30, 7, -13, 28, -27],\n [0, 0, 18, 29, -34, -32, -4, -34, 28, -22, -16, 13],\n [0, 0, 0, -15, -4, -28, -20, 4, -9, -18, -1, 16],\n [0, 0, 0, 0, -5, 25, 28, -2, 19, 23, -33, -19],\n [0, 0, 0, 0, 0, -32, 25, -19, -8, 14, -28, -2],\n [0, 0, 0, 0, 0, 0, -14, -20, -24, 15, -35, -9],\n [0, 0, 0, 0, 0, 0, 0, 1, 29, 6, 13, -32],\n [0, 0, 0, 0, 0, 0, 0, 0, 11, 2, -3, 12],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 13, -22],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -18, -14],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
32
|
MATH
|
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-10, -33, -16, 4, 3, -18, 5, 34, -9, -21, 1, 22],\n [0, -29, 5, -26, 26, -10, 32, -12, 5, 29, -19, -12],\n [0, 0, -24, -33, -26, -3, 10, 23, 16, -30, -34, -7],\n [0, 0, 0, 32, -7, 26, 24, 5, 29, 28, 27, 12],\n [0, 0, 0, 0, -2, 3, 31, 26, -12, -33, 35, 31],\n [0, 0, 0, 0, 0, -22, 32, 28, -16, -8, -22, 8],\n [0, 0, 0, 0, 0, 0, -19, 19, -26, -30, 12, 31],\n [0, 0, 0, 0, 0, 0, 0, 0, -21, 20, -32, 16],\n [0, 0, 0, 0, 0, 0, 0, 0, -15, 7, -26, -6],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 11, 18, -4],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -7],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
32
|
MATH
|
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[7, 18, -4, -8, -10, 14, 4, 8, 12, -16, 16, -18],\n [18, -32, -4, -16, -8, -8, -6, 14, 6, 12, -10, -4],\n [-4, -4, -31, 16, -6, 2, 18, -14, -18, 18, -6, 10],\n [-8, -16, 16, 14, -18, 24, -20, 2, 2, -19, -10, 8],\n [-10, -8, -6, -18, 11, 13, 24, 20, -1, -3, -5, 10],\n [14, -8, 2, 24, 13, -22, 0, -7, -6, -6, -14, -16],\n [4, -6, 18, -20, 24, 0, -12, -8, -6, 10, -11, -12],\n [8, 14, -14, 2, 20, -7, -8, 34, 2, 7, -20, -15],\n [12, 6, -18, 2, -1, -6, -6, 2, -30, 12, -7, 15],\n [-16, 12, 18, -19, -3, -6, 10, 7, 12, -11, -9, 4],\n [16, -10, -6, -10, -5, -14, -11, -20, -7, -9, -28, 30],\n [-18, -4, 10, 8, 10, -16, -12, -15, 15, 4, 30, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
79
|
MATH
|
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[21, 16, -10, 8, 2, -14, 2, -7, -16, 2, -12, -17],\n [16, 22, -15, 0, -4, -16, 8, -18, 18, 14, -8, -20],\n [-10, -15, 21, -6, -6, -27, 28, -32, 16, 21, 4, -18],\n [8, 0, -6, -11, -17, 23, -10, -2, -4, -12, -14, -16],\n [2, -4, -6, -17, -5, -15, 4, -6, 16, 6, 32, 10],\n [-14, -16, -27, 23, -15, -2, 6, 10, -4, 15, -3, -1],\n [2, 8, 28, -10, 4, 6, 16, 0, 23, 18, 24, -2],\n [-7, -18, -32, -2, -6, 10, 0, -18, -6, -10, -22, -4],\n [-16, 18, 16, -4, 16, -4, 23, -6, 16, -34, 6, -2],\n [2, 14, 21, -12, 6, 15, 18, -10, -34, 29, 25, 0],\n [-12, -8, 4, -14, 32, -3, 24, -22, 6, 25, -11, -14],\n [-17, -20, -18, -16, 10, -1, -2, -4, -2, 0, -14, -31]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
100
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[12, -10, -13, 26, -23, -27, -16, 21, -12, -3, -16, 24],\n [0, 28, -6, -19, -22, -17, 35, 23, 31, 8, -4, -25],\n [0, 0, -19, 4, 10, -32, 2, 27, -7, -17, -7, -1],\n [0, 0, 0, 8, 12, 16, -28, 19, 30, 4, -5, 12],\n [0, 0, 0, 0, 19, -23, 1, 11, 35, -14, 3, 22],\n [0, 0, 0, 0, 0, 35, -29, 33, 29, 10, -18, -23],\n [0, 0, 0, 0, 0, 0, 4, -21, -30, 27, -28, -4],\n [0, 0, 0, 0, 0, 0, 0, 26, 25, -35, 30, -4],\n [0, 0, 0, 0, 0, 0, 0, 0, -15, -6, -16, -20],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 22, 5],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 28],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
35
|
MATH
|
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-12, -20, -17, 2, 13, -22, 12, 8, 20, 2, 0, -12],\n [-20, 12, 26, 5, -20, 20, 12, 30, -28, -8, -5, -2],\n [-17, 26, -32, -26, 7, 3, 18, 2, -30, 4, -16, 0],\n [2, 5, -26, -23, 22, 0, 4, -13, -14, 4, 5, 4],\n [13, -20, 7, 22, 7, 5, 14, 4, -12, -15, 11, -2],\n [-22, 20, 3, 0, 5, 33, 14, -18, 12, 32, 2, 4],\n [12, 12, 18, 4, 14, 14, -11, -4, -4, -28, -4, 0],\n [8, 30, 2, -13, 4, -18, -4, -8, 2, -2, 3, -31],\n [20, -28, -30, -14, -12, 12, -4, 2, -30, 0, -4, -4],\n [2, -8, 4, 4, -15, 32, -28, -2, 0, 31, -12, 32],\n [0, -5, -16, 5, 11, 2, -4, 3, -4, -12, -13, 20],\n [-12, -2, 0, 4, -2, 4, 0, -31, -4, 32, 20, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
532
|
MATH
|
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-3, -32, 6, -10, -14, 2, 14, -16, -6, 28, 12, 3],\n [-32, -2, -11, -6, 8, -2, -25, -9, 0, -5, -30, 24],\n [6, -11, 31, 8, -12, -9, 22, 24, 2, 25, -4, -12],\n [-10, -6, 8, 33, 7, 14, 2, -2, -11, -4, -4, -22],\n [-14, 8, -12, 7, -27, -14, -24, 25, -5, 3, -18, 5],\n [2, -2, -9, 14, -14, 17, -4, 4, -6, -5, -6, -17],\n [14, -25, 22, 2, -24, -4, 0, -8, -4, 25, -4, -1],\n [-16, -9, 24, -2, 25, 4, -8, 26, -30, 2, -3, 23],\n [-6, 0, 2, -11, -5, -6, -4, -30, -22, -2, 0, -1],\n [28, -5, 25, -4, 3, -5, 25, 2, -2, 32, -3, -22],\n [12, -30, -4, -4, -18, -6, -4, -3, 0, -3, -31, -15],\n [3, 24, -12, -22, 5, -17, -1, 23, -1, -22, -15, 34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
531
|
MATH
|
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-15, -31, -4, -4, -4, -20, 25, 28, 22, -16, -4, -28],\n [-31, -22, 18, 12, -2, -4, -24, 6, -10, 11, 6, -8],\n [-4, 18, 12, 27, 10, -4, 22, -27, -13, -31, 14, 16],\n [-4, 12, 27, -17, -24, -20, 6, -6, 15, -24, -22, 32],\n [-4, -2, 10, -24, -32, 28, 6, 10, -9, 6, -5, 8],\n [-20, -4, -4, -20, 28, 15, -20, -12, 12, -6, -32, 0],\n [25, -24, 22, 6, 6, -20, 21, 14, 13, 30, 24, 8],\n [28, 6, -27, -6, 10, -12, 14, 5, -26, 20, -8, -2],\n [22, -10, -13, 15, -9, 12, 13, -26, -20, 4, -18, -24],\n [-16, 11, -31, -24, 6, -6, 30, 20, 4, 29, 22, 6],\n [-4, 6, 14, -22, -5, -32, 24, -8, -18, 22, 29, 0],\n [-28, -8, 16, 32, 8, 0, 8, -2, -24, 6, 0, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
660
|
MATH
|
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[-3, 35, -12, 15, -34, -21, -1, 0, 3, -32, 28, -30],\n [0, -6, 31, -21, -19, -18, -17, 33, -12, 12, -6, -21],\n [0, 0, -9, 28, 5, 32, -31, 17, -28, -14, -29, -14],\n [0, 0, 0, -31, 31, -13, 25, -31, -13, -11, -28, -15],\n [0, 0, 0, 0, -17, 17, 16, 11, 18, 8, -29, -35],\n [0, 0, 0, 0, 0, 33, 29, -3, 23, -3, -4, 23],\n [0, 0, 0, 0, 0, 0, 6, 35, -5, 16, -34, 2],\n [0, 0, 0, 0, 0, 0, 0, 27, -15, -31, -1, 32],\n [0, 0, 0, 0, 0, 0, 0, 0, -30, 30, 20, 13],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -11, 5, 35],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23, 0],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
211
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[7, -14, 20, -2, 26, 5, -2, 9, 8, 21, -12, -9],\n [-14, 1, -28, -14, 1, 4, -18, -18, 0, 9, -17, 10],\n [20, -28, 30, -1, -22, 1, 4, 0, 11, -5, -5, 7],\n [-2, -14, -1, 0, 11, -10, 6, 24, 0, -7, 10, -1],\n [26, 1, -22, 11, -5, -10, 8, 0, 7, -13, -5, 16],\n [5, 4, 1, -10, -10, 5, -26, -6, 18, 10, -26, 26],\n [-2, -18, 4, 6, 8, -26, 0, 5, 3, 18, 6, 12],\n [9, -18, 0, 24, 0, -6, 5, -2, 26, 4, 4, 12],\n [8, 0, 11, 0, 7, 18, 3, 26, 27, -20, -6, -13],\n [21, 9, -5, -7, -13, 10, 18, 4, -20, 1, 0, 18],\n [-12, -17, -5, 10, -5, -26, 6, 4, -6, 0, 8, 2],\n [-9, 10, 7, -1, 16, 26, 12, 12, -13, 18, 2, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
76
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[19, 24, -3, -12, -20, -16, 11, -21, 31, 11, -26, 0],\n [24, -15, 21, -4, 0, -14, -27, -8, -20, -4, 12, 0],\n [-3, 21, 29, -28, 10, -10, -5, -3, -9, 0, -2, 24],\n [-12, -4, -28, 21, 20, -26, 4, -9, 8, 6, -3, -20],\n [-20, 0, 10, 20, 15, 4, -15, 16, 4, -16, 10, -14],\n [-16, -14, -10, -26, 4, -7, -9, -2, -16, 8, 2, -21],\n [11, -27, -5, 4, -15, -9, -32, -12, -5, -21, 12, -2],\n [-21, -8, -3, -9, 16, -2, -12, -33, -4, -10, 10, -11],\n [31, -20, -9, 8, 4, -16, -5, -4, 0, 3, 7, -10],\n [11, -4, 0, 6, -16, 8, -21, -10, 3, 6, -22, 15],\n [-26, 12, -2, -3, 10, 2, 12, 10, 7, -22, -4, 26],\n [0, 0, 24, -20, -14, -21, -2, -11, -10, 15, 26, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
89
|
MATH
|
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-28, -7, -14, 34, 25, 7, 13, -7, -5, 17, -2, 2],\n [0, -32, -34, -24, -1, 34, -15, 25, -1, 12, -21, 35],\n [0, 0, 32, -14, -4, -14, -9, -21, 8, -27, -2, -21],\n [0, 0, 0, -17, -20, -28, -3, -18, -1, 7, 14, -33],\n [0, 0, 0, 0, 34, 11, -22, -29, -5, 15, -7, -21],\n [0, 0, 0, 0, 0, 21, -5, -33, 31, 14, -19, 24],\n [0, 0, 0, 0, 0, 0, 30, -21, -1, 33, -9, -29],\n [0, 0, 0, 0, 0, 0, 0, 10, 35, 34, 32, -35],\n [0, 0, 0, 0, 0, 0, 0, 0, -7, -28, -35, -7],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -29, -19, 7],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, -13],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 27]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
34
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[-22, 15, 2, -16, 1, 14, -24, 10, -19, 4, -3, -2],\n [15, -9, 22, -30, 24, 2, -8, 24, 6, -8, -20, 23],\n [2, 22, -5, -6, 24, 7, 22, 12, -5, -4, 16, 14],\n [-16, -30, -6, -19, -2, -8, -14, 12, 10, 18, -5, 4],\n [1, 24, 24, -2, 8, 20, -6, 10, 0, 2, -16, -18],\n [14, 2, 7, -8, 20, -21, -9, 8, -14, -17, 9, -16],\n [-24, -8, 22, -14, -6, -9, 27, -29, -13, 32, -7, 4],\n [10, 24, 12, 12, 10, 8, -29, -15, 18, 6, -30, 10],\n [-19, 6, -5, 10, 0, -14, -13, 18, -19, -19, 3, -24],\n [4, -8, -4, 18, 2, -17, 32, 6, -19, 19, -2, 8],\n [-3, -20, 16, -5, -16, 9, -7, -30, 3, -2, -31, -20],\n [-2, 23, 14, 4, -18, -16, 4, 10, -24, 8, -20, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
559
|
MATH
|
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