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2. Let A be a matrix whose singular value decomposition is given by [0.4 -0.4 -0.4 -0.4 0.6 [100 0 0 0 0.4 -0.4 -0.4 0.6 -0.4 0 10 0 0 -0.4 0.6 -0.4 -0.4 0 0 10 0 0.6 -0.4 -0.4 -0.4 0 0 0 0 0.4 0.4 0.4 0.4 0 0 0 0 A = 0.4 0.4 0.6 0.5 0.5 0.5 0.5] 0.5 -0.5 -0.5 0.5 -0.5 -0.5 0.5 0.5 -0.5 0.5 -0.5 0.5 (a) Find A. (b) Determine rank of A. (c) Find eigenvalues of ATA. (d) Find the orthonormal basis for R(A). (e) Find the orthonormal basis for N(A). (f) Find the matrix B that is the closest matrix of rank 2 to A. Find the distance between A and B using the Frobenius norm.

2. Let A be a matrix whose singular value decomposition is given by [0.4 -0.4 -0.4 -0.4 0.6 [100 0 0 0 0.4 -0.4 -0.4 0.6 -0.4 0 10 0 0 -0.4 0.6 -0.4 -0.4 0 0 10 0 0.6 -0.4 -0.4 -0.4 0 0 0 0 0.4 0.4 0.4 0.4 0 0 0 0 A = 0.4 0.4 0.6 0.5 0.5 0.5 0.5] 0.5 -0.5 -0.5 0.5 -0.5 -0.5 0.5 0.5 -0.5 0.5 -0.5 0.5 (a) Find A. (b) Determine rank of A. (c) Find eigenvalues of ATA. (d) Find the orthonormal basis for R(A). (e) Find the orthonormal basis for N(A). (f) Find the matrix B that is the closest matrix of rank 2 to A. Find the distance between A and B using the Frobenius norm.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.7: The Inverse Of A Matrix
Problem 30E
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2. Let A be a matrix whose singular value decomposition is given by [0.4 -0.4 -0.4 -0.4 0.6 [100 0 0 0 0.4 -0.4 -0.4 0.6 -0.4 0 10 0 0 A = 0.4 -0.4 0.6 -0.4 -0.4 0 0 10 0 0.6 -0.4 -0.4 -0.4 0 0 0 0 0.4 0.4 0 0 0 0 0.4 0.6 0.4 0.4 0.5 0.5 0.5] 0.5 0.5 -0.5 -0.5 0.5 -0.5 -0.5 0.5 0.5 -0.5 0.5 -0.5 0.5 (a) Find A. (b) Determine rank of A. (c) Find eigenvalues of ATA. (d) Find the orthonormal basis for R(A). (e) Find the orthonormal basis for N(A). (f) Find the matrix B that is the closest matrix of rank 2 to A. Find the distance between A and B using the Frobenius norm. 1
Transcribed Image Text:2. Let A be a matrix whose singular value decomposition is given by [0.4 -0.4 -0.4 -0.4 0.6 [100 0 0 0 0.4 -0.4 -0.4 0.6 -0.4 0 10 0 0 A = 0.4 -0.4 0.6 -0.4 -0.4 0 0 10 0 0.6 -0.4 -0.4 -0.4 0 0 0 0 0.4 0.4 0 0 0 0 0.4 0.6 0.4 0.4 0.5 0.5 0.5] 0.5 0.5 -0.5 -0.5 0.5 -0.5 -0.5 0.5 0.5 -0.5 0.5 -0.5 0.5 (a) Find A. (b) Determine rank of A. (c) Find eigenvalues of ATA. (d) Find the orthonormal basis for R(A). (e) Find the orthonormal basis for N(A). (f) Find the matrix B that is the closest matrix of rank 2 to A. Find the distance between A and B using the Frobenius norm. 1
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