QUESTION 21Consider matrix A =-11-11-11-1Suppose the eigenvalues of A and the bases for the corresponding eigenspaces are as follows:11 = 0; E1=0= span,12 = 3; E2=3 = spana) Explain why A is orthogonally diagonalizable.b) Find an orthogonal matrix Q that diagonalizes A and the corresponding diagonal matrixD such that D =Q-¬AQ.c) Find Q-1. Hence, find A5.

step:-1 Part (a):- Spectral Theorem:- A matrix is symmetric if and only if it is orthogonally…

QUESTION 2 1 Consider matrix A = -1 1 -1 1 -1 1 -1 1 Suppose the eigenvalues of A and the bases for the corresponding eigenspaces are as follows: 11 = 0; E3=0 = span ,^2 = 3; E1=3 = span %3D a) Explain why A is orthogonally diagonalizable. b) Find an orthogonal matrix Q that diagonalizes A and the corresponding diagonal matrix D such that D = Q¬'AQ. c) Find Q-1. Hence, find A5.

QUESTION 2 1 Consider matrix A = -1 1 -1 1 -1 1 -1 1 Suppose the eigenvalues of A and the bases for the corresponding eigenspaces are as follows: 11 = 0; E3=0 = span ,^2 = 3; E1=3 = span %3D a) Explain why A is orthogonally diagonalizable. b) Find an orthogonal matrix Q that diagonalizes A and the corresponding diagonal matrix D such that D = Q¬'AQ. c) Find Q-1. Hence, find A5.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.1: Inner Product Spaces

Problem 11AEXP

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