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Suppose a matrix A has singular value decomposition A = UEVT, 0 0 300 0 2 0 0 0 1 where U = 1 0. 0. Σ 0 -1 0 1 0. V = - 0 -1 0 0 1 Use SVD to find the following. (a) Find the best rank 1 approximation to A in the least squares sense. (b) Use SVD to find a basis of range(A) and justify. (c) Use SVD to find a basis of null(A) and justify.

Suppose a matrix A has singular value decomposition A = UEVT, 0 0 300 0 2 0 0 0 1 where U = 1 0. 0. Σ 0 -1 0 1 0. V = - 0 -1 0 0 1 Use SVD to find the following. (a) Find the best rank 1 approximation to A in the least squares sense. (b) Use SVD to find a basis of range(A) and justify. (c) Use SVD to find a basis of null(A) and justify.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Suppose a matrix A has singular value decomposition A = UEVT, 0 0 300 0 2 0 0 0 1 where U = 1 0. 0 -1 0 1 V = 0 -1 0 0 1 Use SVD to find the following. (a) Find the best rank 1 approximation to A in the least squares sense. (b) Use SVD to find a basis of range(A) and justify. (c) Use SVD to find a basis of null(A) and justify.
Transcribed Image Text:Suppose a matrix A has singular value decomposition A = UEVT, 0 0 300 0 2 0 0 0 1 where U = 1 0. 0 -1 0 1 V = 0 -1 0 0 1 Use SVD to find the following. (a) Find the best rank 1 approximation to A in the least squares sense. (b) Use SVD to find a basis of range(A) and justify. (c) Use SVD to find a basis of null(A) and justify.
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