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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 (a) Find A. (b) Determine rank of A. (c) Find eigenvalues of AT A. 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

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 (a) Find A. (b) Determine rank of A. (c) Find eigenvalues of AT A. 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

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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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 -0.4 0.6 [100 0 0 0 -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 -0.4 0 0 0 0 0.4 0 0 0 0 0.4 0.6 -0.4 0.4 0.4 -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 AT A. (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 -0.4 0.6 [100 0 0 0 -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 -0.4 0 0 0 0 0.4 0 0 0 0 0.4 0.6 -0.4 0.4 0.4 -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 AT A. (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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