messages listlengths 1 1 | ground_truth stringclasses 59 values | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, 9, 4, 0, -3, 10],\n [-4, 8, 0, 0, 10, -7],\n [-3, -8, 10, -9, 1, -5],\n [-9, 10, -10, 1, 1, 6],\n [-1, 5, 4, 4, 8, 1],\n [9, -8, -6, 8, -4, 10]]\n... | 24 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, -4, 7, -7, 3, 7],\n [-2, 10, -9, 9, 4, -4],\n [1, -3, 4, -8, 3, 6],\n [-7, 7, -3, -7, -9, -5],\n [-1, -7, 7, 1, -9, -1],\n [-7, 3, 5, 4, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"... | 24 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, 10, 5, 2, 7, 4],\n [10, 2, -2, 4, 2, -10],\n [-4, -2, -10, 1, -3, 0],\n [8, 6, -3, -8, -8, -10],\n [-6, -1, -4, -2, -4, -2],\n [-3, 1, -9, -10, 5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | 23 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-8, 1, -3, -8, -10, -8],\n [-6, 4, 3, -8, -10, -6],\n [3, -4, -2, 4, 4, -1],\n [2, 8, -4, 6, 9, -7],\n [-6, -4, 2, 4, 0, -7],\n [2, -4, 8, -9, -1, 2]]\n\nPresent the answer in LaTex forma... | 25 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[10, -5, 1, 1, 9, 0],\n [-4, -10, -10, 9, 2, -2],\n [-8, -4, -5, -3, -2, -6],\n [-10, 8, -1, 1, 4, -2],\n [9, 6, 6, 9, 1, -4],\n [-9, -8, 6, -6, 6, 6]]... | 18 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[6, -9, -9, -6, -10, -10],\n [8, -9, 10, 1, -5, -7],\n [0, 6, -5, -6, 9, -9],\n [-5, 0, 5, 5, -10, -2],\n [-5, 5, -8, 9, -7, 8],\n [-8, 8, 9, -4, 9, -2]]\n\nPresen... | 27 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-10, -3, -4, 7, -3, -10],\n [0, 7, -1, -8, -4, 5],\n [5, 9, 6, -9, -10, 5],\n [1, -6, -6, -2, -2, -8],\n [8, 5, 5, -8, 9, -10],\n [9, 0, 6, -3, -7, -5]]\n\nPresent the answer in LaTex for... | 27 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, 9, -8, 5, -8, 7],\n [3, 7, -9, -8, 5, -2],\n [-7, -10, -7, -10, 3, 10],\n [5, 9, -3, -4, -8, 6],\n [-10, 5, 1, 8, 3, -5],\n [-5, 2, 8, -3, -9, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 23 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-10, 4, -10, -6, 5, 8],\n [-7, -8, 6, 6, 1, 3],\n [10, -5, -8, -2, -6, 6],\n [3, 10, -8, -10, 9, 10],\n [-10, -8, 7, -1, -8, -3],\n [3, 7, 4, -9, -1, -9]]\n\nPresent the answer in LaTex f... | 30 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, -3, -10, -2, 0, 5],\n [-4, -1, -8, 7, 2, -4],\n [-7, 2, 9, -10, -3, 3],\n [5, 3, 1, 8, 4, -9],\n [-9, 8, 6, 9, -1, -5],\n [4, 0, -6, -10, -3, 10]]\n\nPresent the answer in LaTex format: \\boxed... | 27 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, 1, -6, -4, -7, -5],\n [2, 9, 4, -8, -3, 9],\n [5, 2, 7, -1, 8, 6],\n [8, -6, 10, -2, 1, 10],\n [-10, -10, 4, -9, 5, -3],\n [2, 10, -10, 5, -4, -6]]\n\nPresent ... | 27 | MATH |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-8, 1, 5, 8, -6, 3],\n [-6, 4, 6, 3, 9, -6],\n [1, 5, 5, 10, -4, -7],\n [-10, -6, -1, -6, -7, -9],\n [9, -1, 8, -10, -6, 2],\n [-7, 5, 5, -9, 6, 9]]\n\nPresent the answer in LaTex format: \\boxed{You... | 22 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, 7, -8, -10, -10, 8],\n [0, -6, 1, -8, -10, -10],\n [-3, -1, 0, 1, 2, 1],\n [3, -9, 8, 7, -8, 6],\n [-3, -1, -9, 8, -2, -4],\n [-7, 10, 7, 2, 0, -7]]\n\nPresent the answer in La... | 18 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[10, -7, -1, -6, -2, -8],\n [6, -8, 5, -7, 7, 6],\n [-4, -6, 1, 6, 2, -8],\n [-2, 6, 6, 9, 5, 2],\n [8, 6, -7, 1, -2, 8],\n [1, -2, -4, 3, 9, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 21 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, 5, 10, -6, -8, 1],\n [9, 10, -7, 10, 5, -4],\n [2, 10, -1, -4, 3, -6],\n [-8, 0, 0, 7, 4, 1],\n [-2, -1, 1, 6, -5, -4],\n [3, 2, -3, -1, -2, 7]]\n\nPresent the... | 18 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-9, -6, -6, -5, 8, -3],\n [5, 2, -10, 9, 6, -4],\n [2, -7, -7, -5, 8, 1],\n [-4, -1, 8, -4, -8, 2],\n [2, 7, 9, -3, -2, -4],\n [-10, -8, 2, 6, -10, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}... | 74 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[10, -5, 1, 2, 2, 4],\n [10, 5, 10, 0, -6, -7],\n [-8, 8, 9, 7, 4, -2],\n [6, 3, 4, -10, 10, -8],\n [5, 0, 1, -1, 5, -3],\n [-5, 1, 10, -3, -7, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
... | 22 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[7, -6, -2, -7, 6, -2],\n [-10, 10, 9, 2, 5, 2],\n [3, -8, -5, 7, 8, -6],\n [4, -9, -1, 7, 2, -6],\n [-10, -10, 7, 4, 6, 0],\n [10, 6, 2, -10, -9, -2]]\n\nPresent the answer in LaTex f... | 79 | MATH |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-8, -10, 10, 5, -5, 6],\n [-6, -6, -5, -8, 10, -6],\n [10, -6, -1, -1, 8, 6],\n [10, 3, -2, 3, -10, 8],\n [2, 2, -7, -10, 6, -3],\n [-9, -3, -4, -9, -8, 7]]\n\nPresent the answer in LaTex format: \\b... | 26 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[1, -10, 1, -6, 6, 5],\n [4, 4, -6, 10, 3, -9],\n [0, 8, -4, -5, -9, -5],\n [7, -9, 7, 4, 8, -9],\n [9, -5, -10, 4, -1, 8],\n [6, -6, -7, -1, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"... | 24 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, 9, -6, -9, -5, 10],\n [-9, 2, 0, 0, 5, 0],\n [8, 4, 5, 0, 5, -3],\n [-7, -3, -7, -8, -8, 7],\n [8, 8, 10, -6, 7, -1],\n [10, -5, -10, -6, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 76 | MATH |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, -9, 6, 3, 2, -2],\n [4, 4, 0, 5, 6, -7],\n [-10, -3, 6, -8, 9, 4],\n [4, 3, 3, -9, 2, 3],\n [8, -4, -8, 4, 3, 0],\n [4, 2, 7, -5, -8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer... | 22 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[4, -6, -1, -4, 6, -4],\n [1, 6, 2, 9, -7, -1],\n [-8, -2, 2, 7, 4, -7],\n [4, -9, 4, -3, -3, 6],\n [1, 8, -1, -2, -6, -5],\n [9, -9, 2, -5, -6, -10]]\... | 21 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[10, 10, -5, -5, 5, -7],\n [0, -2, -8, 8, -3, -6],\n [-7, -5, -9, 9, 0, -7],\n [4, -5, 6, -5, 8, -9],\n [4, 0, -3, 8, 2, 1],\n [-6, -5, -7, 8, 9, -10]]\n\nPresent the answer in LaTex f... | 77 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[9, 6, 1, 4, -10, 3],\n [-5, -6, 0, -7, 2, 0],\n [-8, -10, -5, 7, -1, -6],\n [-1, 1, -9, 2, -3, -9],\n [9, -10, -6, -2, 6, -2],\n [0, 4, -5, -8, 6, -6]]\n\nPresent the answer in La... | 22 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, 7, 3, 10, 0, -2],\n [-9, 1, -8, -8, -10, -3],\n [-3, 0, -2, -6, 3, -8],\n [10, -6, -6, 8, 3, -7],\n [2, -1, 7, -3, -3, -4],\n [-3, 3, 8, -5, -10, 4]]\n\nPresent the answer in L... | 24 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-10, 6, -10, 4, -9, 3],\n [10, -3, -3, 8, -4, 8],\n [-5, -5, -8, -4, 8, -3],\n [-1, 9, 4, 4, -10, 9],\n [-4, -7, -5, -10, -6, -10],\n [-7, -9, -1, -6, -1, -10]]\n\nPresent the answer in LaTex form... | 27 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-5, 2, 4, -7, 2, 9],\n [4, -3, -6, 4, -7, 1],\n [2, -9, 8, 8, -7, -7],\n [0, -6, 9, 0, -1, -3],\n [-5, -5, -3, 4, 3, 0],\n [1, 2, -3, 7, -10, 4]]\n\nP... | 22 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, 0, 1, 1, -7, 5],\n [-7, -6, -6, -3, -1, 6],\n [-2, 8, 3, -3, -2, 0],\n [-10, 3, -6, 10, 3, -7],\n [-10, 8, -3, 4, 10, 4],\n [-2, 10, -2, -1, 9, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | 25 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-2, -8, 9, 0, -5, -9],\n [-4, 7, -9, 6, 0, 1],\n [8, -4, 9, -5, 10, -10],\n [6, 0, 7, 10, 6, -4],\n [6, 9, -2, 6, 9, -3],\n [6, -4, -10, 2, 8, 8]]\n\nPresent the answer in LaTex forma... | 81 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, 2, 5, -3, 8, 7],\n [-10, 3, 8, 4, 7, -9],\n [6, 7, -5, 8, -7, -10],\n [-3, -4, -8, -1, -1, 8],\n [3, -9, -10, 7, -4, -3],\n [-10, -8, -3, 4, -6, -8]]\n\nPresent the answer in LaTex for... | 26 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[8, -10, 4, -3, -9, -8],\n [3, 3, 0, 5, -7, 9],\n [-6, 10, 3, 5, 7, -4],\n [-1, -4, -10, 10, 8, 5],\n [8, -7, 7, -9, -10, 4],\n [-6, 9, 0, -1, -9, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",... | 83 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, 9, -6, -6, -5, -2],\n [-9, 10, 1, -8, 9, 1],\n [6, -1, 3, 6, 7, 8],\n [6, 3, -2, -3, -9, 2],\n [-4, -2, 0, 3, -7, 2],\n [-9, -6, 0, -5, 7, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 75 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, -7, -2, -5, -9, 6],\n [-6, -5, 1, 10, -1, 10],\n [-5, -3, -9, 1, 2, 10],\n [-4, -1, 2, 6, 10, 3],\n [-9, 0, -10, 8, 10, -7],\n [8, 10, 0, -3, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 26 | MATH |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, -4, -3, -8, -9, 4],\n [-6, -10, -7, 4, 9, 8],\n [-8, 9, 0, 6, 2, 0],\n [-9, -2, -9, 10, -2, -2],\n [-3, 6, -10, 0, -3, -1],\n [-4, -8, -8, 7, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | 76 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, 8, -5, -9, 1, 8],\n [-6, 1, 6, 6, -1, 6],\n [4, 1, 5, 8, -3, 10],\n [6, -6, 5, -5, -3, 7],\n [1, 4, -2, 2, 4, -1],\n [5, -4, 6, 10, -4, 3]]\n\nPresent the answer in LaTex forma... | 22 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[4, 10, -4, -2, 8, 5],\n [-3, 7, 7, 9, -4, -8],\n [7, -1, -4, 6, 3, -8],\n [1, 2, -9, -8, -6, 0],\n [-3, 1, -4, 4, 6, -7],\n [2, 7, -10, 5, 2, -1]]\n\n... | 15 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[1, -9, -8, -1, -9, 2],\n [2, 7, -8, -4, 3, 9],\n [6, 10, 1, 5, 1, 4],\n [-1, -4, 9, -6, -10, 6],\n [-8, 2, 3, 7, -7, 7],\n [-6, 5, -10, 10, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Yo... | 23 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, 4, 6, -7, 1, -6],\n [-6, 0, -5, -4, 3, 0],\n [2, -9, -4, 9, -7, -3],\n [9, 10, 8, 2, 3, -1],\n [0, -9, -2, 6, -8, -5],\n [-6, -6, 4, 6, -2, -8]]\n\nPresent the answer in LaTex format: \\boxed{... | 25 | MATH |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[9, 6, -1, -8, 7, 7],\n [6, -8, -8, -5, 2, 4],\n [-2, -7, 3, -6, -9, 0],\n [-2, -8, -2, -8, -9, 1],\n [-1, -2, 4, -3, -6, 0],\n [-9, 4, -5, -3, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Y... | 23 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[7, -5, -6, 5, 2, -6],\n [2, 6, 7, -3, 2, 8],\n [-8, -3, -9, -3, 2, 2],\n [-10, -5, 8, 5, -3, -10],\n [5, -2, 2, 0, 2, 10],\n [-1, -7, -5, -4, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 70 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[2, 8, -1, -1, 0, 10],\n [-4, 7, -7, -9, 3, 2],\n [1, -4, -9, 2, 3, 6],\n [-2, 6, -3, -9, 2, -8],\n [5, -5, 8, -4, -1, -2],\n [-9, 4, -6, -7, 9, -7]]\n\nPresent the answer in LaTex format: \\boxed{... | 23 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[7, -7, 6, 1, 6, -1],\n [-10, 7, 7, 3, 4, 1],\n [-7, -8, 9, 1, -4, 0],\n [-10, -5, 4, 4, 8, 0],\n [-9, 3, -9, -7, 6, -8],\n [2, -2, -4, 4, 0, 9]]\n\nPresent the answer in LaTex for... | 20 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[-9, 4, 3, 9, 0, -8],\n [6, 1, 10, 4, 5, -6],\n [9, -5, 8, -6, -8, -10],\n [-5, 4, -9, -8, 6, 1],\n [7, 4, 1, 5, -3, 3],\n [6, 10, -3, 4, 3, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 24 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[9, -4, -8, 1, 10, -8],\n [9, 3, 4, 3, -4, 6],\n [1, 9, -7, -2, -5, 5],\n [10, 10, -9, -3, 0, 2],\n [6, -3, 10, 7, 7, 3],\n [4, -5, 0, 2, -10, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 23 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, -3, 0, 8, -2, 6],\n [1, 3, 4, 5, 9, -10],\n [-1, -3, 7, -10, -9, -10],\n [-10, -2, 2, -10, 2, 9],\n [-4, -9, -5, -4, 3, 7],\n [4, -9, -1, 1, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}... | 78 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, -8, -5, -2, -5, -2],\n [-4, -2, 7, 1, -3, -3],\n [7, 9, 4, -4, 0, 9],\n [5, -7, -5, -8, -2, -1],\n [3, 0, 7, 1, 1, 2],\n [2, 8, 8, 3, -7, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 22 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, 10, 8, 1, 7, -5],\n [7, 8, -6, -2, -8, -1],\n [8, -8, 4, -10, -4, 1],\n [6, 10, 9, -6, -7, 1],\n [9, 7, 6, 8, -2, -7],\n [10, -9, -7, -9, 4, -9]]\n\nPresent the answer in LaTe... | 26 | MATH |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-7, -5, -4, -1, 8, 8],\n [1, -8, 2, 7, -3, 10],\n [4, -10, -8, -3, -7, 5],\n [-1, 1, 3, 3, -9, -6],\n [-6, -5, 2, -2, 4, 3],\n [-4, 9, -9, -4, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Y... | 21 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-9, -8, -6, -6, -10, -3],\n [1, -7, 2, 4, 0, -1],\n [-8, 3, 5, -1, -1, 1],\n [-2, -10, -6, 9, -3, 0],\n [1, -10, 9, 0, -6, 4],\n [-6, 1, -6, 6, 6, 1]]\n\nPresent the answer in LaTex format: \\box... | 70 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, 4, -5, 1, 9, 7],\n [3, -9, -2, -6, 9, -10],\n [-8, -5, -6, 10, -6, -10],\n [6, 8, 3, 1, -1, 9],\n [10, 7, 0, -9, 7, -4],\n [4, 0, 7, 1, -5, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 27 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, 9, 5, 7, -1, -3],\n [7, 10, -10, -3, -5, -6],\n [4, 4, -9, -10, 0, -1],\n [7, 7, 6, -3, 4, -3],\n [6, 1, -3, 3, -7, -10],\n [-10, 8, 5, 3, 10, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 26 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, -2, -9, 7, -5, -2],\n [-10, -2, 5, 2, -2, 10],\n [2, -2, 0, -7, -9, -5],\n [3, -7, -5, 8, -5, -9],\n [7, 2, -2, 8, 2, 0],\n [-10, -4, 10, 4, -10, 1]]\n\nPresent the answer in ... | 20 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, 4, 10, 8, -10, 6],\n [6, -8, 1, -5, 0, -8],\n [-3, 3, 3, -1, -9, 3],\n [-2, -8, 10, -3, 5, -9],\n [-5, 10, 1, -6, -9, 5],\n [-6, 4, 1, -7, 4, 0]]\n\nPresent t... | 26 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[5, -5, 3, 7, 1, 0],\n [2, 10, 0, 5, 4, 10],\n [4, -7, 0, 8, 4, -7],\n [10, 2, 8, -9, 3, -7],\n [5, 10, 9, 3, 4, -8],\n [-3, 5, -1, -7, 7, -9]]\n\nPresent the answ... | 23 | MATH |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, 2, -7, 0, -4, 1],\n [-1, -4, 2, -4, 6, -1],\n [-1, -7, 9, -7, -4, -10],\n [1, 2, -1, 4, 2, 10],\n [-2, -2, 4, -1, -1, -3],\n [5, 6, -6, -7, 7, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | 56 | MATH |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-7, -4, -1, 7, 8, -7],\n [-1, -10, 7, -6, 4, 6],\n [-8, 1, -9, -10, 10, 6],\n [5, -6, 4, -8, -4, 0],\n [-1, -2, 3, 2, -9, -8],\n [-4, 10, 7, -8, -1, -4]]\n\nPresent the answer in LaTex format: \\boxe... | 23 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, 6, 0, -4, 3, 8],\n [-7, -5, -1, -4, 2, 3],\n [-7, -3, -6, -10, -7, -8],\n [-2, -3, -10, -5, -2, -4],\n [-7, 2, 6, -9, -6, 1],\n [10, -3, -5, -3, 7, -8]]\n\nPresent the answer in LaTex... | 22 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, -8, -5, -9, 1, -9],\n [-5, 6, -8, -9, 9, -3],\n [1, -7, -6, 2, 4, 5],\n [-1, 5, 1, 6, 5, 1],\n [-3, 9, -8, 5, 2, 8],\n [-3, -6, 9, -3, 1, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 25 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[10, 9, -5, 7, -3, -4],\n [-10, 10, 5, 1, -5, 9],\n [-9, 3, -7, -10, 7, 2],\n [-9, -2, 10, -9, -2, -10],\n [0, -8, 9, -7, 7, -5],\n [-8, 0, 4, -6, 9, -1]]\n\nPresent the answer in LaTex format: \\b... | 27 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, 4, 6, -1, -5, 7],\n [2, -8, -1, 3, -5, -8],\n [5, -4, 9, 3, -2, 4],\n [10, -8, -9, -9, -8, 7],\n [3, 9, 7, -1, -9, -10],\n [-7, 3, -10, 3, 5, 3]]\n\nPresent th... | 20 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[9, -8, -8, -2, -5, 2],\n [10, -9, -3, 10, -9, -7],\n [4, -7, 2, 1, 2, 3],\n [9, 7, -5, 0, -9, 8],\n [8, -6, 8, -9, -1, -9],\n [0, 7, 4, -2, 8, -2]]\n\... | 21 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-8, 10, -2, 3, 8, -4],\n [5, 5, -10, -7, -7, -4],\n [-3, 6, -6, -4, 9, 9],\n [-7, -5, -4, 7, -6, 9],\n [-8, -4, 3, -4, -6, -6],\n [-9, 10, -5, 4, 10, -1]]\n\nPresent the answer in LaTex format: \... | 83 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, -6, -10, 2, 10, 7],\n [2, 10, 10, 7, -6, 2],\n [-7, 6, -8, 6, 0, 10],\n [9, 10, -7, -9, 9, 5],\n [7, -3, -8, -2, 9, -5],\n [-1, 10, -1, 2, 6, -2]]\n\nPresent ... | 22 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, -2, -2, -10, -9, 5],\n [-10, -1, 7, -3, 10, 0],\n [-9, -3, -3, 6, 4, 6],\n [2, 8, -6, 1, -10, -6],\n [-3, 2, -3, 0, -10, 2],\n [8, -8, 6, -6, 9, 10]]\n\nPresent the answer in L... | 25 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-3, 3, -7, 0, 9, 4],\n [8, -4, 8, 8, 0, -6],\n [-6, -3, -1, -5, 4, 5],\n [6, -3, -3, -2, -9, 4],\n [7, -8, 6, -7, -7, 3],\n [-2, -2, 7, -1, 10, -7]]\n... | 21 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, -3, -9, 2, 10, 5],\n [-9, 0, -1, 4, 6, -3],\n [7, -2, -3, 3, 7, 9],\n [9, 10, 1, 8, 3, 6],\n [10, -8, -4, 6, 1, -2],\n [4, 7, 10, 2, 10, -3]]\n\nPr... | 20 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, -3, 3, -4, 1, 0],\n [0, 2, 7, -9, 10, 4],\n [9, 7, 4, 8, 1, 2],\n [0, -6, -10, -8, 8, -4],\n [1, 4, -6, 4, -3, -1],\n [5, -3, -10, 1, -6, -8]]\n\nPresent the answer in LaTex fo... | 21 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-10, -7, -3, -8, -1, -9],\n [0, -1, 10, 3, -4, -9],\n [-2, 5, 2, -2, 9, -7],\n [-1, 1, 6, 3, 3, -9],\n [10, 9, 0, 5, 8, -5],\n [8, -6, -7, 4, -7, 9]]\n\nPresent the answer in LaTe... | 25 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, -8, -6, -5, 10, -3],\n [-4, 10, -1, -5, 3, -7],\n [2, 9, 6, -4, -7, 3],\n [-8, -6, 5, 9, -7, -9],\n [7, 8, 8, 6, 3, 8],\n [2, 1, -5, 10, -7, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"... | 24 | MATH |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, 2, -7, 6, -10, 7],\n [9, 6, 4, 0, 2, -10],\n [6, -5, -7, 9, 5, 4],\n [4, -5, 4, 3, 0, -4],\n [-2, 5, -6, 9, -1, 7],\n [-8, 2, 0, 6, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 74 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, 2, 8, 10, 8, -1],\n [-8, 3, 8, -6, -6, 9],\n [6, 10, -1, -6, -7, -5],\n [-7, -4, -4, 7, -8, -10],\n [-7, -5, -2, 3, 1, 9],\n [-7, 10, 1, -1, -4, -8]]\n\nPresent the answer in LaTex... | 85 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, -1, 5, 5, -1, 2],\n [-5, 1, -2, 2, -7, 0],\n [9, 7, 0, 10, -7, 7],\n [-10, -4, -5, 4, 7, 0],\n [9, 4, 5, -4, 10, -1],\n [1, 3, -6, 10, 7, -6]]\n\nPresent the answer in LaTex fo... | 19 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-8, -6, 6, 8, 8, 10],\n [1, -2, -10, 7, 10, -7],\n [-1, -4, -10, 6, -9, 0],\n [-2, -4, 6, 6, -9, -5],\n [3, -5, -9, -10, -1, 10],\n [-6, -9, 5, -9, -1, -9]]\n\nPresent the answer in LaTex format: ... | 18 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[5, 5, 8, -4, 1, 4],\n [-3, -5, -1, -8, 8, 6],\n [-4, 10, 9, -7, 3, 9],\n [4, -3, 10, 4, 9, 3],\n [-2, -3, 6, -9, -8, -3],\n [1, -10, -1, 9, -8, -5]]\n... | 23 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-4, 9, 7, 0, 8, -6],\n [8, 0, 1, -1, -3, -2],\n [-7, -6, 10, -3, -2, 4],\n [4, 5, 3, -3, 7, -1],\n [9, -5, 1, -9, -4, 5],\n [-8, 2, -8, 7, 0, -3]]\n\nPresent the answer in LaTex f... | 22 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, -10, -10, -3, -6, 5],\n [0, -6, -7, -5, 3, 8],\n [-2, 1, 0, 3, 5, -10],\n [2, 10, 10, 2, -9, -7],\n [-5, -6, -8, -10, -7, 9],\n [-9, -6, -8, -2, 9, -5]]\n\nPresent the answer in LaTex format: ... | 32 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[7, -5, 8, 1, 0, -9],\n [4, 1, 1, -2, 10, -9],\n [-8, 1, 5, 10, -10, 10],\n [-8, 9, -9, -2, 8, 4],\n [7, 0, 5, 6, -6, 1],\n [0, 4, -8, -10, 9, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 28 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-9, -9, -8, -3, 4, -4],\n [-5, -2, 9, -10, -3, -8],\n [-7, 4, -5, 4, 10, -8],\n [10, 10, 3, 9, 3, -7],\n [1, 6, -4, -2, -8, 2],\n [4, 7, 8, -10, -5, -9]]\n\nPresent the answer in LaTex fo... | 25 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, -5, 3, -7, 10, -3],\n [-8, 8, 3, 9, 6, -3],\n [3, -5, 5, 8, 3, 8],\n [-8, -1, 8, -2, 9, 2],\n [-4, 3, -2, 8, 4, 9],\n [3, -5, 10, -7, -3, 6]]\n\nPresent the answer in LaTex for... | 20 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-2, -10, 9, 3, 0, 10],\n [-8, -2, 3, -2, -7, -7],\n [-3, -9, -2, 3, -2, 5],\n [6, 5, 1, -8, 0, 3],\n [7, 10, 10, -6, 5, 9],\n [-6, -8, 1, -10, 10, -2]]\n\nPresent the answer in LaTex ... | 80 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, -7, -8, 6, -9, -10],\n [-3, 2, 4, -3, 1, 1],\n [3, 4, 4, -2, 8, 9],\n [-3, 10, 8, -5, 9, 8],\n [-7, -4, -7, 1, 2, -8],\n [1, -9, -9, -2, -10, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 34 | MATH |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, -5, 7, 6, 1, -5],\n [-3, 8, -1, -10, 2, 6],\n [-8, -3, 3, -8, 5, 2],\n [9, 6, 2, -5, 6, 3],\n [6, -3, 0, 9, -10, -4],\n [10, 10, 6, -1, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 69 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, -6, 6, -2, 6, 10],\n [8, -4, -2, -4, 2, 0],\n [3, 8, 0, 2, 3, 2],\n [-10, -3, 1, 8, 1, -3],\n [-3, 10, 2, 1, 5, -10],\n [2, -4, -6, -3, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[4, 6, 4, 9, 7, 7],\n [-9, -7, -10, -7, 7, -6],\n [8, 4, -3, 9, 6, -10],\n [1, 8, 4, -2, -4, -9],\n [-2, -1, -9, 8, 0, 2],\n [-1, 3, 7, 8, -2, -4]]\n\n... | 19 | MATH |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-8, 9, -5, 10, -9, -5],\n [-8, 5, -3, -9, 6, -2],\n [1, -8, 0, -10, 2, 4],\n [-6, 10, 6, -5, 10, 0],\n [7, -7, -8, 2, -2, 10],\n [-5, 1, -9, -8, -8, 1]]\n\nPresent the answer in LaTex format: \\boxed... | 25 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, -2, -3, 0, 5, -7],\n [-10, -4, -9, -6, -4, -7],\n [-6, -10, -10, 4, 9, 8],\n [-1, 7, -8, 0, 4, 0],\n [6, 6, -5, -6, -3, -9],\n [5, 9, 1, -5, -10, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | 28 | MATH |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, 2, 7, -6, -8, 0],\n [2, -7, 3, 0, -1, 8],\n [7, -5, 4, 10, -1, -6],\n [-6, -1, -6, -8, -5, -7],\n [7, -2, 6, 2, 4, 9],\n [6, 2, 5, -7, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your ... | 22 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, 6, 2, -9, 2, 10],\n [8, -8, -1, -9, 2, 8],\n [6, 10, 3, 1, 10, 1],\n [0, -4, -7, 8, -10, -8],\n [2, 4, -9, 0, -7, 8],\n [6, -8, 7, -3, 8, -6]]\n\nPresent the answer in LaTex format: \\boxed{Yo... | 25 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, 10, -3, -6, 6, -6],\n [-7, 8, 10, -9, 0, 2],\n [4, 1, 10, 0, -4, -6],\n [6, 9, -2, 3, 1, -5],\n [6, 8, 8, 5, 1, 1],\n [9, -5, -7, -5, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Y... | 77 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, 0, 8, 7, 6, 8],\n [10, 3, 7, 8, 4, 4],\n [-7, -4, 2, -8, 5, -2],\n [-3, 9, 2, 6, 6, 6],\n [-10, -3, 8, -5, -8, -6],\n [2, 4, 3, 5, 7, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 28 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-8, -1, -1, 10, 5, 1],\n [-9, -2, -8, 4, -8, 8],\n [7, -3, 6, -3, -4, -4],\n [-8, -10, -7, -6, -10, 4],\n [-6, 2, -3, -3, -6, -2],\n [-10, -7, -8, -9, -3, -2]]\n\nPresent the answ... | 28 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-9, 3, 3, -7, -5, 0],\n [-8, -3, -8, 3, 2, 2],\n [-9, 2, 8, -5, 5, -9],\n [-3, 6, -9, -1, 5, -5],\n [-9, -9, 2, 4, -9, -4],\n [-8, -3, 3, -4, 10, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",... | 77 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-10, 6, -2, 10, 2, 10],\n [8, 10, 8, 6, -1, -1],\n [-7, -3, 9, 9, 7, 3],\n [7, 3, 9, 10, 4, -7],\n [2, -3, 7, 1, 3, -9],\n [7, -9, 0, -2, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{You... | 79 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, 6, 7, -5, 6, 7],\n [-3, -2, -5, -6, 1, 0],\n [-10, 0, 8, -2, -9, 1],\n [-7, -7, 7, 4, 8, 2],\n [8, 6, -5, 5, 1, 8],\n [-6, 6, -10, -1, 4, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 22 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[10, 0, 2, -6, -10, 1],\n [0, 6, -7, 4, -2, 10],\n [9, 8, 8, 1, -6, -1],\n [6, -6, 5, -4, -2, -8],\n [4, 5, 7, 3, -8, 1],\n [-2, -4, -2, 2, 7, -6]]\n\nPresent the answer in LaTex format: \... | 25 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, -7, -9, 5, -2, -2],\n [-5, 0, -10, -7, 2, 2],\n [2, -9, -2, -3, -4, -7],\n [7, -8, -5, 1, 1, 10],\n [-3, -10, -7, 10, 0, -8],\n [2, 6, -1, 10, 1, 4]]\n\nPresent the answer in LaTex... | 72 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[10, -1, 3, 2, -6, -5],\n [-9, 6, -7, 3, -1, -8],\n [-8, 4, -5, 6, 1, 9],\n [0, -7, -5, -10, 9, 5],\n [4, 6, -3, 1, 10, -1],\n [4, -2, -9, -6, -5, -4]]\n\nPresent the answer in LaTex format: \\boxe... | 19 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[10, -10, -4, 9, 1, 5],\n [5, 0, 10, -7, 2, -4],\n [-7, 4, 8, -2, 0, -3],\n [-10, -3, 2, -7, -3, -8],\n [-2, -9, -9, 2, 4, 1],\n [-7, -3, -2, -6, 9, 7]]\n\nPresent the answer in LaTex format: \\box... | 23 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, 4, -2, 6, 1, -4],\n [-1, -1, 2, 8, 0, 2],\n [10, -3, -3, -7, 4, 0],\n [0, -10, 6, 4, 9, -5],\n [4, -2, 3, 7, 6, 7],\n [-6, 9, 9, -2, 0, -10]]\n\nPresent the answer in LaTex format: \\b... | 20 | MATH |
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