messages listlengths 1 1 | ground_truth stringclasses 65 values | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[1, -9, 4, 0],\n [-9, 7, 8, -4],\n [4, 8, 8, -9],\n [0, -4, -9, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-1, 6, -3, -1],\n [6, 3, -10, 4],\n [-3, -10, 11, -2],\n [-1, 4, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[2, 12, 8, 4],\n [12, -2, 1, -6],\n [8, 1, 12, -7],\n [4, -6, -7, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 22 | MATH |
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-2, -4, 2, 0],\n [-4, 9, -6, 2],\n [2, -6, -9, -2],\n [0, 2, -2, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 34 | MATH |
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-9, -1, 8, 6],\n [0, 7, -12, -12],\n [0, 0, -7, -7],\n [0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 31 | MATH |
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[-7, 5, 6, 0],\n [5, -11, 1, 6],\n [6, 1, 6, -4],\n [0, 6, -4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 16 | MATH |
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[9, -6, 5, -6],\n [-6, 7, 11, 8],\n [5, 11, 10, 8],\n [-6, 8, 8, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 24 | MATH |
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-12, -2, 0, 4],\n [-2, 10, -5, -4],\n [0, -5, -4, 2],\n [4, -4, 2, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 42 | MATH |
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[1, -2, 8, 6],\n [-2, -3, -2, -10],\n [8, -2, 8, 2],\n [6, -10, 2, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 16 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[8, -2, 10, 0],\n [-2, -2, 2, 2],\n [10, 2, 12, -2],\n [0, 2, -2, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 34 | MATH |
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-4, 6, -9, 3],\n [0, 6, -5, -1],\n [0, 0, -5, 11],\n [0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-12, 2, 0, -5],\n [2, 1, -4, 2],\n [0, -4, -3, 0],\n [-5, 2, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 14 | MATH |
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-5, 0, -3, -4],\n [0, 12, 0, -2],\n [-3, 0, 6, -4],\n [-4, -2, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 31 | MATH |
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[3, -8, -11, -10],\n [0, 8, 1, -4],\n [0, 0, -6, -1],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[-1, 3, 7, 0],\n [0, -3, 10, -8],\n [0, 0, 7, 6],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 17 | MATH |
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-3, -10, 4, 7],\n [0, -11, -10, 4],\n [0, 0, 4, 8],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[-9, -1, 10, 10],\n [0, 2, -12, -12],\n [0, 0, -12, 4],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 27 | MATH |
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[-10, 8, -10, 1],\n [8, -4, -1, 0],\n [-10, -1, -2, -10],\n [1, 0, -10, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 45 | MATH |
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-8, -2, 10, -3],\n [-2, 12, 0, -4],\n [10, 0, -3, -4],\n [-3, -4, -4, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 42 | MATH |
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[6, 3, 2, 4],\n [3, -8, 3, 0],\n [2, 3, -1, 8],\n [4, 0, 8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 34 | MATH |
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-10, -7, -11, 0],\n [0, -9, -12, 8],\n [0, 0, -10, 6],\n [0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 38 | MATH |
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-9, 5, -10, 2],\n [0, -4, -7, -10],\n [0, 0, 9, 6],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 23 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[2, 3, -2, -2],\n [3, 7, -4, -1],\n [-2, -4, 1, 2],\n [-2, -1, 2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 21 | MATH |
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-7, 10, 0, -4],\n [10, 3, -2, 1],\n [0, -2, -12, -3],\n [-4, 1, -3, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 17 | MATH |
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-6, 9, -1, -8],\n [0, -5, -10, 11],\n [0, 0, 6, 1],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7 | MATH |
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[8, 1, -8, -8],\n [0, 8, -10, 0],\n [0, 0, -11, 11],\n [0, 0, 0, -7]]\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[[5, -8, 0, 2],\n [-8, -8, 0, -4],\n [0, 0, -3, -4],\n [2, -4, -4, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12 | MATH |
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[10, 6, 8, 2],\n [6, -8, 3, -2],\n [8, 3, -3, -6],\n [2, -2, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 16 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[9, 1, -9, 5],\n [1, 1, 0, 0],\n [-9, 0, 11, 0],\n [5, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[11, 4, -7, -4],\n [4, 12, -4, 5],\n [-7, -4, 12, 2],\n [-4, 5, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 22 | MATH |
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[-1, 6, 8, -2],\n [6, 3, -2, 10],\n [8, -2, -12, -4],\n [-2, 10, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 17 | MATH |
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[9, -10, -2, 12],\n [0, -9, -5, -5],\n [0, 0, -11, 12],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 37 | MATH |
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[12, -2, 2, 0],\n [-2, 12, -2, 0],\n [2, -2, 7, -1],\n [0, 0, -1, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 38 | MATH |
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-11, 2, 11, 2],\n [0, 11, -10, 2],\n [0, 0, 2, -5],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 27 | MATH |
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[8, 0, 5, 6],\n [0, 1, 6, -4],\n [5, 6, 1, -4],\n [6, -4, -4, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 13 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-3, -10, -5, -9],\n [-10, 5, -10, 4],\n [-5, -10, -11, 8],\n [-9, 4, 8, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 23 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[-4, -5, -7, -9],\n [0, 5, 5, 4],\n [0, 0, 4, -8],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 23 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[12, -2, -2, -3],\n [-2, -5, -5, 1],\n [-2, -5, -1, -6],\n [-3, 1, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 13 | MATH |
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[5, 2, 4, -10],\n [2, -6, -4, 4],\n [4, -4, -7, -6],\n [-10, 4, -6, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 43 | MATH |
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[10, -2, -4, 10],\n [-2, 5, -4, 6],\n [-4, -4, -2, -4],\n [10, 6, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 17 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-8, -4, 8, 0],\n [-4, 3, 6, 6],\n [8, 6, -5, -1],\n [0, 6, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 17 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-11, -6, -6, 8],\n [-6, -8, -1, 1],\n [-6, -1, 8, -2],\n [8, 1, -2, -7]]\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[[-10, 4, 8, -7],\n [4, 2, -2, 1],\n [8, -2, -12, 4],\n [-7, 1, 4, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 38 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-8, 0, -10, 11],\n [0, -11, -1, 7],\n [0, 0, -8, 0],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11 | MATH |
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[10, 7, 8, -4],\n [0, -8, 4, -8],\n [0, 0, 8, -8],\n [0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[8, 9, -8, -2],\n [9, 11, 0, -12],\n [-8, 0, -12, 3],\n [-2, -12, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 25 | MATH |
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-5, -1, -6, 1],\n [-1, 4, 3, 4],\n [-6, 3, 5, -3],\n [1, 4, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[4, 0, -1, 3],\n [0, -8, -5, -5],\n [-1, -5, -9, -4],\n [3, -5, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 27 | MATH |
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[1, 2, 11, 10],\n [0, 4, -11, 7],\n [0, 0, 0, 10],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[9, -5, 10, -2],\n [0, 9, -2, 0],\n [0, 0, 3, -7],\n [0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9 | MATH |
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[12, 10, 6, -8],\n [10, -4, -6, 4],\n [6, -6, -10, 0],\n [-8, 4, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 19 | MATH |
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-1, 4, -2, 0],\n [4, -10, 4, 0],\n [-2, 4, 11, 8],\n [0, 0, 8, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 15 | MATH |
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[10, -1, -10, 5],\n [-1, 8, -6, 0],\n [-10, -6, 6, -2],\n [5, 0, -2, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-7, 2, 10, 0],\n [2, -9, 0, 6],\n [10, 0, 12, 0],\n [0, 6, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 16 | MATH |
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-11, -2, 6, 2],\n [-2, 10, 1, -2],\n [6, 1, -3, -6],\n [2, -2, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 36 | MATH |
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[0, -2, 7, -1],\n [-2, -9, 8, -2],\n [7, 8, 6, 3],\n [-1, -2, 3, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 39 | MATH |
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-4, -2, 10, -2],\n [-2, 0, -1, 8],\n [10, -1, 6, -4],\n [-2, 8, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 39 | MATH |
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-4, -3, -7, 5],\n [0, -6, -5, 1],\n [0, 0, -3, 10],\n [0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6 | MATH |
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-7, 0, 2, 7],\n [0, 8, 4, -4],\n [2, 4, -10, -2],\n [7, -4, -2, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 16 | MATH |
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-2, -8, 10, -5],\n [-8, -11, -6, 9],\n [10, -6, 10, 8],\n [-5, 9, 8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[0, -6, 0, -2],\n [-6, -5, 4, -4],\n [0, 4, 0, -7],\n [-2, -4, -7, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 16 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[7, 6, 6, 8],\n [6, 4, -11, -8],\n [6, -11, 7, 2],\n [8, -8, 2, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 23 | MATH |
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[3, -8, 10, 3],\n [-8, 11, 4, -6],\n [10, 4, 8, -6],\n [3, -6, -6, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[8, -10, 3, -5],\n [0, 11, 7, 6],\n [0, 0, -10, 4],\n [0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 37 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-6, -2, 2, -6],\n [-2, -7, -3, -8],\n [2, -3, -6, 8],\n [-6, -8, 8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 18 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[-3, 0, 6, -5],\n [0, -4, 6, 6],\n [6, 6, 5, -10],\n [-5, 6, -10, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[4, -2, -2, -4],\n [-2, -5, 2, -6],\n [-2, 2, -10, -5],\n [-4, -6, -5, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 16 | MATH |
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-6, 8, -8, -10],\n [0, 7, -5, 4],\n [0, 0, 5, 2],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[9, -2, 8, -1],\n [-2, -12, -2, -5],\n [8, -2, -11, -1],\n [-1, -5, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 15 | MATH |
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[-3, -2, 2, 2],\n [-2, -11, 4, -2],\n [2, 4, 3, -6],\n [2, -2, -6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 15 | MATH |
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-12, 10, 8, -2],\n [10, -5, 3, 10],\n [8, 3, 9, -5],\n [-2, 10, -5, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 58 | MATH |
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[-10, 10, 10, 4],\n [10, 10, 2, -6],\n [10, 2, -2, 6],\n [4, -6, 6, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 19 | MATH |
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-11, 1, -9, 9],\n [0, -5, -1, 12],\n [0, 0, -2, 9],\n [0, 0, 0, 2]]\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[[5, 0, 3, -2],\n [0, 6, -2, -7],\n [3, -2, -10, -2],\n [-2, -7, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 31 | MATH |
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[10, 2, -7, 3],\n [2, -9, 4, -9],\n [-7, 4, 9, -4],\n [3, -9, -4, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 48 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[6, -8, 10, -9],\n [0, 10, -7, 5],\n [0, 0, 3, -8],\n [0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 28 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[-6, -3, 4, 2],\n [-3, 3, 0, -6],\n [4, 0, 5, -4],\n [2, -6, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 30 | MATH |
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-12, 6, -11, 2],\n [6, 7, -3, 2],\n [-11, -3, 6, 9],\n [2, 2, 9, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 54 | MATH |
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-2, -3, 3, -1],\n [0, 9, -12, 4],\n [0, 0, -5, -12],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9 | MATH |
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[7, -11, 1, -9],\n [0, 1, 12, 11],\n [0, 0, 12, -10],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12 | MATH |
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[9, -6, 3, 2],\n [-6, 2, 6, -6],\n [3, 6, -9, -11],\n [2, -6, -11, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 47 | MATH |
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-5, 5, -3, -4],\n [5, 4, 4, 8],\n [-3, 4, 0, -2],\n [-4, 8, -2, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 31 | MATH |
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[11, 12, 3, -2],\n [12, 2, -1, 4],\n [3, -1, 0, -2],\n [-2, 4, -2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[-2, -4, 0, 0],\n [-4, 5, 0, -8],\n [0, 0, 7, -5],\n [0, -8, -5, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 16 | MATH |
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-4, 4, 1, -7],\n [4, 0, -1, -3],\n [1, -1, 2, -4],\n [-7, -3, -4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 14 | MATH |
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-9, 8, 5, -4],\n [8, 2, -10, 6],\n [5, -10, 4, 0],\n [-4, 6, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 41 | MATH |
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[3, -11, 7, 4],\n [-11, 4, 0, 4],\n [7, 0, 2, 2],\n [4, 4, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 38 | MATH |
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-10, 0, 0, 6],\n [0, 11, 0, -4],\n [0, 0, -8, -12],\n [6, -4, -12, -1]]\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[[-6, 6, -8, 8],\n [6, 11, 6, -2],\n [-8, 6, -3, -5],\n [8, -2, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 49 | MATH |
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[2, -4, -2, -5],\n [-4, 11, -4, 0],\n [-2, -4, 4, -2],\n [-5, 0, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 14 | MATH |
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-8, 2, 10, 0],\n [2, 3, -1, -4],\n [10, -1, 9, -1],\n [0, -4, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 14 | MATH |
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[6, 1, -10, 10],\n [1, -11, -4, -6],\n [-10, -4, 12, 0],\n [10, -6, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 52 | MATH |
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-12, 4, -1, 0],\n [4, -3, -7, 1],\n [-1, -7, 1, -6],\n [0, 1, -6, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 14 | MATH |
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[12, -6, 0, 5],\n [-6, 6, -5, -8],\n [0, -5, 6, -2],\n [5, -8, -2, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 22 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-11, 2, -9, -4],\n [2, -3, -8, -6],\n [-9, -8, 10, 4],\n [-4, -6, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 19 | MATH |
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[5, -1, 6, -11],\n [0, 12, -9, -7],\n [0, 0, -11, 7],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12 | MATH |
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-12, 7, 4, -1],\n [0, -5, -11, -1],\n [0, 0, 2, -6],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12 | MATH |
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[4, 2, 0, 10],\n [2, 6, 3, -10],\n [0, 3, 8, 4],\n [10, -10, 4, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 21 | MATH |
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[2, 4, 3, 2],\n [4, -4, -7, 10],\n [3, -7, 7, -1],\n [2, 10, -1, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 17 | MATH |
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[-4, 8, 1, 6],\n [8, -5, -2, -11],\n [1, -2, 1, -9],\n [6, -11, -9, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
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