-1 3.) Given the matrix A 0 -2 2 1 (a) Find the singular values o; of A. [Hint: first show that the characteristic polynomial of (AT A) is X³ – 13 X² +36 A.] (b) Find the rank 1 matrix A' that is closest to A (with respect to the Frobenius norm). Note: you do NOT necd to find the whole SVD to do this. Find only those parts you need for A'. (c) Find both the Frobenius norm ||A||F and the 2-norm ||A||2 of A. Note: the matrix 2-norm is subordinate to the vector 2-norm.

-1 3.) Given the matrix A 0 -2 2 1 (a) Find the singular values o; of A. [Hint: first show that the characteristic polynomial of (AT A) is X³ – 13 X² +36 A.] (b) Find the rank 1 matrix A' that is closest to A (with respect to the Frobenius norm). Note: you do NOT necd to find the whole SVD to do this. Find only those parts you need for A'. (c) Find both the Frobenius norm ||A||F and the 2-norm ||A||2 of A. Note: the matrix 2-norm is subordinate to the vector 2-norm.

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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