Consider the matrix A = [-120 5]. (a) Determine the SVD of A by hand. (b) List the singular values, left singular vectors, and right singular vectors of A. Draw a careful, labeled picture of the unit circle in R² and its image under A, together with the singular vectors, with the coordinates of their vertices marked. (c) What are the 1-, 2-, -, and Frobenius norms of A? (d) Use the SVD to find A-¹. (You must show your work and how you used SVD.)

Consider the matrix A = [-120 5]. (a) Determine the SVD of A by hand. (b) List the singular values, left singular vectors, and right singular vectors of A. Draw a careful, labeled picture of the unit circle in R² and its image under A, together with the singular vectors, with the coordinates of their vertices marked. (c) What are the 1-, 2-, -, and Frobenius norms of A? (d) Use the SVD to find A-¹. (You must show your work and how you used SVD.)

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter5: Orthogonality

Section5.3: The Gram-schmidt Process And The Qr Factorization

Problem 23EQ

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