messages listlengths 1 1 | ground_truth stringclasses 104 values | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[15, 2, 4, -8, -9, 3],\n [2, 2, -3, 2, 8, -6],\n [4, -3, -11, 4, -2, 2],\n [-8, 2, 4, -12, -2, -1],\n [-9, 8, -2, -2, 11, -11],\n [3, -6, 2, -1, -11, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 28 | MATH |
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[6, 1, -9, -5, -12, -11],\n [0, -5, -15, 9, -6, 4],\n [0, 0, -5, 8, 15, 1],\n [0, 0, 0, 11, 4, 2],\n [0, 0, 0, 0, -11, 2],\n [0, 0, 0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 48 | MATH |
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[3, -5, 6, 5, -8, -8],\n [-5, -1, 6, 2, -14, 2],\n [6, 6, 9, -10, -2, 0],\n [5, 2, -10, -14, 2, 4],\n [-8, -14, -2, 2, 11, 4],\n [-8, 2, 0, 4, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | 88 | MATH |
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[11, -6, 0, 10, -2, 4],\n [-6, 3, 4, -6, 10, 0],\n [0, 4, -15, 11, 6, -2],\n [10, -6, 11, 11, -5, 6],\n [-2, 10, 6, -5, 11, 0],\n [4, 0, -2, 6, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 30 | MATH |
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[12, 5, -2, -3, -2, -6],\n [5, 5, -6, 6, 6, -3],\n [-2, -6, -1, 1, 0, 4],\n [-3, 6, 1, -4, -4, -2],\n [-2, 6, 0, -4, -12, 11],\n [-6, -3, 4, -2, 11, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | 24 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-15, -8, 0, -1, 6, 0],\n [-8, 0, -4, 3, 4, 4],\n [0, -4, 5, 12, 0, 8],\n [-1, 3, 12, 8, 6, -3],\n [6, 4, 0, 6, 1, -9],\n [0, 4, 8, -3, -9, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}... | 25 | MATH |
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[11, -10, 8, 12, -2, 1],\n [-10, 1, -3, 10, 2, -6],\n [8, -3, 5, 8, 2, -2],\n [12, 10, 8, 4, 0, 8],\n [-2, 2, 2, 0, 13, -6],\n [1, -6, -2, 8, -6, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | 27 | MATH |
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-3, 3, 0, 6, -7, -7],\n [3, 1, 4, 0, 9, 1],\n [0, 4, 5, 0, 4, 8],\n [6, 0, 0, 2, 4, -10],\n [-7, 9, 4, 4, 6, 2],\n [-7, 1, 8, -10, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
... | 65 | MATH |
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[12, -2, 10, 5, -6, 4],\n [-2, -14, 10, 0, -4, 8],\n [10, 10, -3, 2, -6, 2],\n [5, 0, 2, -2, 5, 11],\n [-6, -4, -6, 5, 6, 6],\n [4, 8, 2, 11, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | 25 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[9, 15, -5, 2, 7, -12],\n [15, 2, -9, 12, 1, -6],\n [-5, -9, -12, 6, -2, 8],\n [2, 12, 6, -3, -6, -13],\n [7, 1, -2, -6, 6, -2],\n [-12, -6, 8, -13, -2, 12]]\n\nPresent the answer in LaTex format: \\b... | 94 | MATH |
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[-10, -1, 0, -7, 0, -8],\n [-1, -15, -10, 1, -2, -1],\n [0, -10, 8, 0, -8, 4],\n [-7, 1, 0, 6, 6, 2],\n [0, -2, -8, 6, 0, 6],\n [-8, -1, 4, 2, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | 21 | MATH |
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-11, -3, -10, 12, 11, 14],\n [0, 1, -9, -10, -14, -5],\n [0, 0, 5, -8, -11, 11],\n [0, 0, 0, -2, -4, 1],\n [0, 0, 0, 0, -9, -2],\n [0, 0, 0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 32 | MATH |
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[15, 5, -4, 7, 3, 0],\n [5, 1, 7, 8, 3, 0],\n [-4, 7, 0, -10, 4, 1],\n [7, 8, -10, -3, 0, 6],\n [3, 3, 4, 0, 10, -1],\n [0, 0, 1, 6, -1, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 22 | MATH |
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[9, 6, -14, 0, -1, 8],\n [6, -3, 8, -11, -7, 6],\n [-14, 8, -5, -4, 2, 15],\n [0, -11, -4, -13, 12, -4],\n [-1, -7, 2, 12, -4, 10],\n [8, 6, 15, -4, 10, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 27 | MATH |
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[6, 4, 4, -5, -2, 9],\n [4, -15, 0, 8, 6, -1],\n [4, 0, -14, 2, 6, -5],\n [-5, 8, 2, -6, -4, 8],\n [-2, 6, 6, -4, -8, 8],\n [9, -1, -5, 8, 8, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | 78 | MATH |
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-4, 1, -10, 5, 6, -4],\n [1, -15, 9, 2, 8, -8],\n [-10, 9, -14, -4, 4, -7],\n [5, 2, -4, -6, -6, -7],\n [6, 8, 4, -6, 10, 4],\n [-4, -8, -7, -7, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"... | 27 | MATH |
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[5, 2, -3, 5, 2, 10],\n [2, 11, 2, -5, 10, 2],\n [-3, 2, -6, -6, 1, -6],\n [5, -5, -6, -10, 1, 2],\n [2, 10, 1, 1, 14, -6],\n [10, 2, -6, 2, -6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | 24 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-9, 10, 8, 4, -10, 2],\n [10, -7, -4, -2, 6, 1],\n [8, -4, 10, 0, -2, -9],\n [4, -2, 0, 5, -1, 8],\n [-10, 6, -2, -1, 1, -1],\n [2, 1, -9, 8, -1, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your an... | 25 | MATH |
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-9, 6, 4, 1, -1, -5],\n [6, 9, -2, -7, -14, -12],\n [4, -2, 0, -1, -2, -1],\n [1, -7, -1, 3, -7, -12],\n [-1, -14, -2, -7, 7, -4],\n [-5, -12, -1, -12, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 82 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[3, -4, -4, -6, 8, 1],\n [-4, -8, -10, 0, -10, 3],\n [-4, -10, 5, -1, 0, -4],\n [-6, 0, -1, 13, 0, -2],\n [8, -10, 0, 0, -2, 5],\n [1, 3, -4, -2, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed... | 71 | MATH |
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-6, -4, 12, -6, 11, -8],\n [-4, -10, -4, -6, 0, -4],\n [12, -4, -7, 2, 10, -1],\n [-6, -6, 2, -4, 7, -2],\n [11, 0, 10, 7, 3, 0],\n [-8, -4, -1, -2, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 24 | MATH |
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[5, 1, 8, -5, 0, 2],\n [1, 11, -6, 8, 0, 8],\n [8, -6, 1, -8, 4, -8],\n [-5, 8, -8, -13, -2, 4],\n [0, 0, 4, -2, -15, -2],\n [2, 8, -8, 4, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 24 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[-1, 2, -8, 4, 4, -8],\n [2, -8, -10, -4, 4, -6],\n [-8, -10, -1, -4, -4, 6],\n [4, -4, -4, -5, 4, 13],\n [4, 4, -4, 4, -4, 0],\n [-8, -6, 6, 13, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{... | 79 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[6, -5, -6, -6, -10, 9],\n [-5, 2, -10, -6, -2, -2],\n [-6, -10, -12, 11, -4, 2],\n [-6, -6, 11, -6, -4, 5],\n [-10, -2, -4, -4, 10, 1],\n [9, -2, 2, 5, 1, 0]]\n\nPresent the answer in LaTex format: \... | 85 | MATH |
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[12, -12, -4, -5, -13, 15],\n [0, 14, -11, -10, 3, 2],\n [0, 0, -5, -11, -7, 15],\n [0, 0, 0, -8, -10, -12],\n [0, 0, 0, 0, 5, 0],\n [0, 0, 0, 0, 0, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | 15 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[-3, -10, -10, -10, -9, -2],\n [-10, -14, -12, 6, 4, -7],\n [-10, -12, -4, 2, 0, 0],\n [-10, 6, 2, -7, 1, 0],\n [-9, 4, 0, 1, -4, 1],\n [-2, -7, 0, 0, 1, -8]]\n\nPresent the answer in LaTex format: \\... | 83 | MATH |
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[7, -10, 5, 4, -9, -13],\n [0, 2, 1, -5, -14, 9],\n [0, 0, 8, 3, -9, 15],\n [0, 0, 0, -9, 12, 5],\n [0, 0, 0, 0, -11, -4],\n [0, 0, 0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 49 | MATH |
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[2, 4, -7, -12, 5, 11],\n [0, -15, 1, 9, -7, 4],\n [0, 0, -3, -7, 14, 4],\n [0, 0, 0, 12, 9, -11],\n [0, 0, 0, 0, -2, -7],\n [0, 0, 0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | 43 | MATH |
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-12, 9, -6, -13, 7, -9],\n [0, -3, -12, 2, -5, 9],\n [0, 0, -2, 2, -8, 11],\n [0, 0, 0, -9, -4, 9],\n [0, 0, 0, 0, -12, -1],\n [0, 0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | 12 | MATH |
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[-1, 6, 0, -4, 0, 1],\n [6, -4, 8, -3, -15, 2],\n [0, 8, -1, -2, 6, -8],\n [-4, -3, -2, 5, -2, 4],\n [0, -15, 6, -2, -7, 2],\n [1, 2, -8, 4, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 27 | MATH |
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[-6, 5, 8, 0, 1, -9],\n [5, 1, 2, 2, 4, 8],\n [8, 2, -9, -8, 2, 0],\n [0, 2, -8, -2, -8, -6],\n [1, 4, 2, -8, -8, 2],\n [-9, 8, 0, -6, 2, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 19 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[-15, -8, -10, 7, -2, 12],\n [-8, -7, -7, 0, 0, -6],\n [-10, -7, -3, 0, -4, -2],\n [7, 0, 0, 3, -2, 7],\n [-2, 0, -4, -2, 9, -1],\n [12, -6, -2, 7, -1, 14]]\n\nPresent the answer in LaTex format: \\bo... | 75 | MATH |
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[1, -10, -2, -2, 8, 3],\n [-10, 0, 4, 2, 6, -3],\n [-2, 4, 4, 2, 14, 5],\n [-2, 2, 2, -4, 0, 10],\n [8, 6, 14, 0, 0, -2],\n [3, -3, 5, 10, -2, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | 20 | MATH |
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[12, -4, 3, 8, -6, 1],\n [-4, -2, -4, -2, 2, 10],\n [3, -4, -13, 12, 0, -4],\n [8, -2, 12, 4, 0, 2],\n [-6, 2, 0, 0, 3, 10],\n [1, 10, -4, 2, 10, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 23 | MATH |
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[1, 4, 10, -8, -5, 4],\n [4, 5, 6, -4, -10, 12],\n [10, 6, 11, -14, -8, 14],\n [-8, -4, -14, -7, -8, 11],\n [-5, -10, -8, -8, -9, 0],\n [4, 12, 14, 11, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",... | 37 | MATH |
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[14, 9, -3, 0, -9, 0],\n [0, -2, 1, -4, 13, 8],\n [0, 0, -3, 8, 4, -1],\n [0, 0, 0, 6, -14, 12],\n [0, 0, 0, 0, 14, 10],\n [0, 0, 0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | 51 | MATH |
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[8, 4, -5, 10, -6, 13],\n [0, -11, -7, 4, 3, -3],\n [0, 0, 11, -10, -6, -14],\n [0, 0, 0, 12, 5, -3],\n [0, 0, 0, 0, -2, -11],\n [0, 0, 0, 0, 0, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | 58 | MATH |
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-1, -9, -7, -11, -9, 4],\n [0, -13, -14, 5, 6, 15],\n [0, 0, 3, -12, 8, 4],\n [0, 0, 0, -9, 1, 3],\n [0, 0, 0, 0, -2, -1],\n [0, 0, 0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 13 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[-6, 0, 1, -4, 8, 2],\n [0, -2, 10, -1, 8, 2],\n [1, 10, -8, -4, 2, -12],\n [-4, -1, -4, -2, 2, 6],\n [8, 8, 2, 2, -10, 5],\n [2, 2, -12, 6, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your... | 72 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[6, -13, 4, -7, 5, 6],\n [-13, -5, 2, 2, 0, 0],\n [4, 2, 5, 8, 2, 6],\n [-7, 2, 8, -8, -12, 0],\n [5, 0, 2, -12, 11, 6],\n [6, 0, 6, 0, 6, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",... | 27 | MATH |
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[15, -4, 2, 2, -6, 11],\n [-4, -3, -13, 0, 5, 0],\n [2, -13, -15, 8, 12, -6],\n [2, 0, 8, 1, 6, -1],\n [-6, 5, 12, 6, -8, -9],\n [11, 0, -6, -1, -9, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"... | 31 | MATH |
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[12, 4, -2, 4, 4, -6],\n [4, 3, -12, 6, -4, 8],\n [-2, -12, -14, -2, 4, 6],\n [4, 6, -2, 3, 4, -7],\n [4, -4, 4, 4, 5, 0],\n [-6, 8, 6, -7, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 76 | MATH |
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[6, 2, 2, 6, -14, -2],\n [2, 7, -4, -6, -6, 11],\n [2, -4, -2, -12, -4, 1],\n [6, -6, -12, -14, -2, 0],\n [-14, -6, -4, -2, -6, 0],\n [-2, 11, 1, 0, 0, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 25 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[-2, 4, -5, 0, 6, 2],\n [4, 4, -3, 6, 1, 2],\n [-5, -3, 4, 8, -2, 0],\n [0, 6, 8, -15, 8, -10],\n [6, 1, -2, 8, -12, -4],\n [2, 2, 0, -10, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your ... | 68 | MATH |
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[7, 9, 14, 6, 4, 6],\n [0, 4, 7, -7, -13, -13],\n [0, 0, -2, 1, -3, 3],\n [0, 0, 0, 11, 9, -2],\n [0, 0, 0, 0, -10, 11],\n [0, 0, 0, 0, 0, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 49 | MATH |
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[0, -5, 7, 8, -4, 6],\n [-5, -3, 2, 0, -13, 3],\n [7, 2, -7, 10, 0, 8],\n [8, 0, 10, -12, 4, -2],\n [-4, -13, 0, 4, 8, -2],\n [6, 3, 8, -2, -2, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | 84 | MATH |
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[-3, 2, 2, 4, -4, 4],\n [2, 13, 6, -6, 10, 4],\n [2, 6, 9, 2, -10, 2],\n [4, -6, 2, 5, 1, -6],\n [-4, 10, -10, 1, 5, 0],\n [4, 4, 2, -6, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | 71 | MATH |
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[9, -8, 10, 2, -8, 4],\n [-8, 3, 0, 6, 4, 4],\n [10, 0, 4, 4, -12, -6],\n [2, 6, 4, -14, 8, -8],\n [-8, 4, -12, 8, -1, 6],\n [4, 4, -6, -8, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 27 | MATH |
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-8, -10, -8, -14, 3, 0],\n [0, -6, -4, 1, -9, 6],\n [0, 0, -12, -13, 3, -1],\n [0, 0, 0, -7, -3, 2],\n [0, 0, 0, 0, 2, -8],\n [0, 0, 0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 40 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[5, 5, 11, 3, 7, 3],\n [0, 3, -5, -13, -8, 4],\n [0, 0, 0, -11, 4, -7],\n [0, 0, 0, -9, -1, 8],\n [0, 0, 0, 0, 1, -10],\n [0, 0, 0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answe... | 21 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[14, 7, 13, -10, 13, -11],\n [0, -15, 13, 2, -1, 7],\n [0, 0, -11, 8, 13, -3],\n [0, 0, 0, 13, -14, -7],\n [0, 0, 0, 0, -15, -4],\n [0, 0, 0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{... | 79 | MATH |
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-1, 4, -2, 2, 10, 4],\n [4, 3, 12, -1, 12, -9],\n [-2, 12, -9, -4, -6, 3],\n [2, -1, -4, -12, 4, -12],\n [10, 12, -6, 4, -6, -4],\n [4, -9, 3, -12, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 25 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-15, 10, 6, -8, -10, 0],\n [10, -7, -8, 2, 2, 2],\n [6, -8, -5, -1, -8, -3],\n [-8, 2, -1, 0, -6, 4],\n [-10, 2, -8, -6, -13, 3],\n [0, 2, -3, 4, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{You... | 32 | MATH |
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[14, 2, 11, -2, -4, 0],\n [2, 10, 0, 0, 9, -2],\n [11, 0, 4, 6, -2, 7],\n [-2, 0, 6, 0, 10, 1],\n [-4, 9, -2, 10, 4, -1],\n [0, -2, 7, 1, -1, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | 78 | MATH |
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[7, 0, 5, -7, -2, 10],\n [0, 15, -2, -2, -2, 2],\n [5, -2, -14, 8, -9, 8],\n [-7, -2, 8, 12, 7, -12],\n [-2, -2, -9, 7, 15, 0],\n [10, 2, 8, -12, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 98 | MATH |
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-7, 2, 3, -4, 15, 15],\n [0, 10, -4, -4, 2, -7],\n [0, 0, 0, 1, 5, 8],\n [0, 0, 0, -14, -8, -4],\n [0, 0, 0, 0, -3, 6],\n [0, 0, 0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | 35 | MATH |
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-10, -2, 13, -12, 6, 12],\n [-2, 9, 6, 4, 2, 8],\n [13, 6, 10, -2, -1, 2],\n [-12, 4, -2, -4, -2, 10],\n [6, 2, -1, -2, 4, 10],\n [12, 8, 2, 10, 10, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 32 | MATH |
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[14, 9, 10, -12, 1, -14],\n [0, 8, -2, 10, -8, -2],\n [0, 0, 0, -12, -15, 7],\n [0, 0, 0, -8, 9, 12],\n [0, 0, 0, 0, 6, 10],\n [0, 0, 0, 0, 0, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | 50 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[14, 8, 3, -9, -13, -8],\n [0, -15, -2, -10, -6, 9],\n [0, 0, -12, -10, 0, 12],\n [0, 0, 0, -15, -10, -7],\n [0, 0, 0, 0, -5, -1],\n [0, 0, 0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your... | 15 | MATH |
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[3, -4, -14, 1, -13, -6],\n [0, 6, -7, -5, 5, -1],\n [0, 0, 14, 5, 5, 5],\n [0, 0, 0, -11, -9, -7],\n [0, 0, 0, 0, -4, 4],\n [0, 0, 0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 46 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-8, 8, 8, 8, -15, -10],\n [0, 9, 8, 3, 11, 1],\n [0, 0, 15, 2, 7, 12],\n [0, 0, 0, -8, -1, -7],\n [0, 0, 0, 0, -3, -15],\n [0, 0, 0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"... | 15 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[-14, 12, -1, -2, 0, -8],\n [12, -10, -10, 2, -11, -6],\n [-1, -10, 14, 4, -9, 12],\n [-2, 2, 4, 11, -8, -6],\n [0, -11, -9, -8, -12, 3],\n [-8, -6, 12, -6, 3, 13]]\n\nPresent the answer in LaTex form... | 102 | MATH |
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-14, -2, -1, 8, 8, 8],\n [-2, 10, 2, -10, 0, 8],\n [-1, 2, -10, 12, -6, -9],\n [8, -10, 12, 11, -8, 9],\n [8, 0, -6, -8, -1, 6],\n [8, 8, -9, 9, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | 26 | MATH |
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-9, 9, -6, 14, -6, -14],\n [0, -3, 6, 13, -10, -7],\n [0, 0, 15, -3, -11, -2],\n [0, 0, 0, -9, -8, 6],\n [0, 0, 0, 0, -8, -15],\n [0, 0, 0, 0, 0, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 58 | MATH |
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-1, 0, 10, 6, -1, 12],\n [0, 6, 7, -2, -5, -1],\n [10, 7, 11, 2, 9, 2],\n [6, -2, 2, -9, 7, 2],\n [-1, -5, 9, 7, -5, 1],\n [12, -1, 2, 2, 1, -3]]\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[[10, 2, -6, 3, 4, 1],\n [0, 0, -11, -13, 14, 11],\n [0, 0, -14, -3, 6, -8],\n [0, 0, 0, 1, -12, 3],\n [0, 0, 0, 0, -1, 12],\n [0, 0, 0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 33 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[5, 4, 7, 0, 14, -2],\n [4, 10, -4, 6, -6, -6],\n [7, -4, -15, -12, -6, 6],\n [0, 6, -12, 12, -6, 12],\n [14, -6, -6, -6, 11, -4],\n [-2, -6, 6, 12, -4, -13]]\n\nPresent the answer in LaTex format: \\... | 104 | MATH |
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-13, 14, -4, 11, 5, 14],\n [0, -10, 5, 12, -10, -8],\n [0, 0, 4, 13, 0, -10],\n [0, 0, 0, -7, 3, 2],\n [0, 0, 0, 0, -10, -4],\n [0, 0, 0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 13 | MATH |
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-15, 8, 1, 13, 13, 4],\n [8, -7, 2, 7, -2, 6],\n [1, 2, 4, -3, 0, 0],\n [13, 7, -3, -12, -10, -3],\n [13, -2, 0, -10, 12, 15],\n [4, 6, 0, -3, 15, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 94 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[15, -3, 3, -8, -6, -8],\n [-3, -7, 0, -4, 2, 5],\n [3, 0, 10, -7, 12, 2],\n [-8, -4, -7, 5, 3, -8],\n [-6, 2, 12, 3, -4, -2],\n [-8, 5, 2, -8, -2, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your ... | 23 | MATH |
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[-8, -7, -14, 1, 4, -3],\n [0, -6, -4, 1, 5, -10],\n [0, 0, -1, -9, 14, -10],\n [0, 0, 0, -13, 10, 9],\n [0, 0, 0, 0, 6, 12],\n [0, 0, 0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | 13 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[-8, -3, -6, 2, -7, 14],\n [0, -3, 2, -1, -14, -5],\n [0, 0, -2, 6, -1, -2],\n [0, 0, 0, -1, 15, 3],\n [0, 0, 0, 0, -5, 12],\n [0, 0, 0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your a... | 23 | MATH |
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[2, 10, -11, -8, -6, 0],\n [10, -8, 9, 1, 2, -4],\n [-11, 9, 1, 7, -2, 6],\n [-8, 1, 7, -2, -8, 5],\n [-6, 2, -2, -8, 4, 14],\n [0, -4, 6, 5, 14, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | 88 | MATH |
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[-12, -8, 0, -3, -4, 12],\n [-8, -8, 6, 1, 10, 0],\n [0, 6, 6, 2, -5, 1],\n [-3, 1, 2, -11, 5, -5],\n [-4, 10, -5, 5, 9, 2],\n [12, 0, 1, -5, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | 86 | MATH |
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-1, -4, 3, 0, 10, 9],\n [-4, 10, -2, -3, 4, 9],\n [3, -2, 0, -4, 1, -3],\n [0, -3, -4, 8, 3, -2],\n [10, 4, 1, 3, -7, 1],\n [9, 9, -3, -2, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 20 | MATH |
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-8, -6, 2, 2, 4, 5],\n [-6, -9, 2, -4, -4, 10],\n [2, 2, -3, -4, -6, 0],\n [2, -4, -4, 6, -6, 0],\n [4, -4, -6, -6, 8, -1],\n [5, 10, 0, 0, -1, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | 70 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[-2, 0, -9, 5, 5, 8],\n [0, 12, 7, 12, -2, 9],\n [0, 0, -12, 2, -13, -15],\n [0, 0, 0, 0, 14, -11],\n [0, 0, 0, 0, -13, 1],\n [0, 0, 0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your a... | 50 | MATH |
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-7, -10, 2, 2, 9, 10],\n [0, -2, -2, -2, 9, -12],\n [0, 0, -1, 2, -2, 10],\n [0, 0, 0, 4, -6, -6],\n [0, 0, 0, 0, 12, 11],\n [0, 0, 0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 35 | MATH |
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-7, 0, -11, -14, 12, 7],\n [0, 2, 9, 9, 3, -3],\n [0, 0, 4, 3, 1, -11],\n [0, 0, 0, 4, -15, -6],\n [0, 0, 0, 0, 3, -10],\n [0, 0, 0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | 7 | MATH |
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[9, 10, 0, -2, -7, 2],\n [10, 0, -1, 0, 6, -2],\n [0, -1, -2, -2, 3, -3],\n [-2, 0, -2, 5, 4, 1],\n [-7, 6, 3, 4, 12, -10],\n [2, -2, -3, 1, -10, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 25 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-14, 0, 0, -2, 10, -2],\n [0, 15, -2, -8, 0, -3],\n [0, -2, -1, 4, -4, 7],\n [-2, -8, 4, -2, 5, -8],\n [10, 0, -4, 5, -5, 1],\n [-2, -3, 7, -8, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your a... | 23 | MATH |
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[11, -1, 0, -2, 12, 7],\n [-1, 13, -8, 2, 0, -12],\n [0, -8, -15, 4, 2, 6],\n [-2, 2, 4, -11, 0, -4],\n [12, 0, 2, 0, -5, 4],\n [7, -12, 6, -4, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | 26 | MATH |
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[3, 0, -6, -12, -10, -5],\n [0, -11, 0, 12, -2, -2],\n [-6, 0, -11, 2, -2, -6],\n [-12, 12, 2, 5, -3, 2],\n [-10, -2, -2, -3, 3, -1],\n [-5, -2, -6, 2, -1, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}... | 21 | MATH |
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[9, -12, -7, 11, -3, -7],\n [0, 5, 3, -2, 15, 5],\n [0, 0, -11, 5, 2, -2],\n [0, 0, 0, -1, -9, -2],\n [0, 0, 0, 0, -8, -14],\n [0, 0, 0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | 45 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[14, 6, 4, 0, -9, -9],\n [0, 2, -14, -1, -2, 15],\n [0, 0, -7, -2, -11, -5],\n [0, 0, 0, -5, -11, 1],\n [0, 0, 0, 0, 6, -14],\n [0, 0, 0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answe... | 14 | MATH |
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[-6, 7, 12, 2, 2, -4],\n [7, -3, 0, -3, -2, 0],\n [12, 0, 0, 4, -2, -3],\n [2, -3, 4, -11, -4, -6],\n [2, -2, -2, -4, -10, 6],\n [-4, 0, -3, -6, 6, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 70 | MATH |
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[4, -10, 0, 4, 8, -13],\n [0, 3, 3, 8, -12, -15],\n [0, 0, 14, 10, 13, -3],\n [0, 0, 0, 3, 6, 8],\n [0, 0, 0, 0, 1, -6],\n [0, 0, 0, 0, 0, 8]]\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[[-1, -10, 0, 7, 6, 0],\n [-10, -10, -10, -8, 4, -1],\n [0, -10, 5, -7, 14, -6],\n [7, -8, -7, -2, 7, -8],\n [6, 4, 14, 7, 3, 4],\n [0, -1, -6, -8, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | 30 | MATH |
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[-4, 6, 2, -8, -5, 14],\n [6, 2, 8, -7, 4, -6],\n [2, 8, 2, -13, -3, -10],\n [-8, -7, -13, 3, -10, 9],\n [-5, 4, -3, -10, -8, 0],\n [14, -6, -10, 9, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | 33 | MATH |
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[0, -4, -6, -8, 3, 7],\n [-4, -7, -10, 8, 8, -5],\n [-6, -10, -13, -3, 7, 7],\n [-8, 8, -3, -5, 2, 14],\n [3, 8, 7, 2, 4, -2],\n [7, -5, 7, 14, -2, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 90 | MATH |
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-11, -6, -6, -2, -14, -12],\n [0, 2, -3, 3, -11, 4],\n [0, 0, -5, 14, 14, 10],\n [0, 0, 0, 7, 12, -6],\n [0, 0, 0, 0, -5, 3],\n [0, 0, 0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | 11 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-2, 10, 0, -2, 10, -5],\n [10, -12, 2, 1, -9, -1],\n [0, 2, 10, 14, 2, -4],\n [-2, 1, 14, 11, 0, -2],\n [10, -9, 2, 0, 3, 10],\n [-5, -1, -4, -2, 10, -7]]\n\nPresent the answer in LaTex format: \\boxed{Yo... | 27 | MATH |
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-9, -8, -1, 3, -1, -11],\n [0, -9, -10, 11, 3, 9],\n [0, 0, -6, 3, 15, 15],\n [0, 0, 0, -6, -5, 7],\n [0, 0, 0, 0, 9, -5],\n [0, 0, 0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | 9 | MATH |
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-1, -2, -2, 8, -4, 8],\n [-2, 13, 0, -8, -1, 2],\n [-2, 0, 15, -4, 6, 8],\n [8, -8, -4, 5, -14, -14],\n [-4, -1, 6, -14, -10, -9],\n [8, 2, 8, -14, -9, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 29 | MATH |
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-3, 10, -4, -4, 6, -3],\n [0, -2, 6, 14, -4, 4],\n [0, 0, -10, 11, -6, 4],\n [0, 0, 0, -7, -14, -9],\n [0, 0, 0, 0, -15, 6],\n [0, 0, 0, 0, 0, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 15 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[-15, -11, 2, 0, 15, 10],\n [0, 14, -12, -15, 7, -8],\n [0, 0, 8, 1, 15, -9],\n [0, 0, 0, 13, 6, -1],\n [0, 0, 0, 0, 9, 5],\n [0, 0, 0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your an... | 60 | MATH |
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[5, -13, 0, 9, -3, 8],\n [-13, -2, -4, 0, -10, -10],\n [0, -4, -9, 0, -3, -1],\n [9, 0, 0, -3, 3, -8],\n [-3, -10, -3, 3, 6, -4],\n [8, -10, -1, -8, -4, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 26 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[7, -6, 0, -7, -4, 4],\n [-6, 13, 0, 6, 2, -12],\n [0, 0, 8, 4, 3, -10],\n [-7, 6, 4, 15, -11, -2],\n [-4, 2, 3, -11, 7, 11],\n [4, -12, -10, -2, 11, -13]]\n\nPresent the answer in LaTex format: \\box... | 93 | MATH |
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-5, -13, 12, -6, 2, -15],\n [0, 0, 11, -6, -15, -12],\n [0, 0, -4, 9, -4, -3],\n [0, 0, 0, 0, -3, -11],\n [0, 0, 0, 0, -4, 3],\n [0, 0, 0, 0, 0, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 14 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[5, -6, -6, 0, 3, 8],\n [-6, -10, -14, 5, -3, 10],\n [-6, -14, -6, 10, -8, -4],\n [0, 5, 10, -14, 8, 14],\n [3, -3, -8, 8, 10, -6],\n [8, 10, -4, 14, -6, -11]]\n\nPresent the answer in LaTex format: \... | 101 | MATH |
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