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Given that the matrix A has the Singular Value Decomposition A = UVT, where: U= 3 Σ = 6000 0400 0000 Answer the questions below using the given SVD, without actually computing the entries in A. You should be able to answer all but the last part below without any calculation. (a) For this m x n matrix A, what is m and what is n? (b) What is the rank r of A? (c) Write down an orthonormal basis for R(A).

Given that the matrix A has the Singular Value Decomposition A = UVT, where: U= 3 Σ = 6000 0400 0000 Answer the questions below using the given SVD, without actually computing the entries in A. You should be able to answer all but the last part below without any calculation. (a) For this m x n matrix A, what is m and what is n? (b) What is the rank r of A? (c) Write down an orthonormal basis for R(A).

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 23EQ
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Linear Algebra 

I would like the answers for subquestions a, b, c. 

Given that the matrix A has the Singular Value Decomposition A = UEVT, where: 6 0 0 0 0 4 0 0 0 0 0 0 U = V = Answer the questions below using the given SVD, without actually computing the entries in A. You should be able to answer all but the last part below without any calculation. (a) For this m x n matrix A, what is m and what is n? (b) What is the rank r of A? (c) Write down an orthonormal basis for R(A). (d) Write down an orthonormal basis for N(A). (e) Write down an orthonormal basis for R(A"). (f) Write down an orthonormal basis for N(A"). (g) Write down the compact form of the SVD of A (as in page 345, item 7). (h) Find the rank 1 matrix A' that is closest to A (with respect to the Frobenius norm).
Transcribed Image Text:Given that the matrix A has the Singular Value Decomposition A = UEVT, where: 6 0 0 0 0 4 0 0 0 0 0 0 U = V = Answer the questions below using the given SVD, without actually computing the entries in A. You should be able to answer all but the last part below without any calculation. (a) For this m x n matrix A, what is m and what is n? (b) What is the rank r of A? (c) Write down an orthonormal basis for R(A). (d) Write down an orthonormal basis for N(A). (e) Write down an orthonormal basis for R(A"). (f) Write down an orthonormal basis for N(A"). (g) Write down the compact form of the SVD of A (as in page 345, item 7). (h) Find the rank 1 matrix A' that is closest to A (with respect to the Frobenius norm).
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