Do Question 5(g) only QUESTION 5Given the matrix A =-1(193-3-1a) Find all the eigenvalues of the matrix A.b) Find the smallest eigenvalues of A5.c) Find the eigenvalues of A¹.d) Find the eigenvalues of A-¹ which are positive.e) Determine the basis for the eigenspace that corresponds to the largest eigenvalue of thematrix A.f) Given the basis for the eigenspace corresponding to eigenvalues λ = -2 and λ = 2 of thematrix A are4and{}}respectively.i) Is the matrix A diagonalizable? Give reason(s) for your answer.ii) If matrix A is diagonalizable, state the matrices P and D such that P-¹AP = D.g) Without using a determinant method, give reason(s) why matrix A is invertible?

Answered: Image /qna-images/answer/4d5cdac0-1378-45f6-b000-c0838d6d338f.jpg

Given the matrix A = 1 -1 -1 3 1 1 -3 1 -1. a) Find all the eigenvalues of the matrix A. b) Find the smallest eigenvalues of AS. c) Find the eigenvalues of AT. d) Find the eigenvalues of A-¹ which are positive. e) Determine the basis for the eigenspace that corresponds to the largest eigenval matrix A. f) Given the basis for the eigenspace corresponding to eigenvalues λ = -2 and λ = 4-6 and matrix A are respectively. i) Is the matrix A diagonalizable? Give reason(s) for your answer. ii) If matrix A is diagonalizable, state the matrices P and D such that P-¹AP = D g) Without using a determinant method, give reason(s) why matrix A is invertible?

Given the matrix A = 1 -1 -1 3 1 1 -3 1 -1. a) Find all the eigenvalues of the matrix A. b) Find the smallest eigenvalues of AS. c) Find the eigenvalues of AT. d) Find the eigenvalues of A-¹ which are positive. e) Determine the basis for the eigenspace that corresponds to the largest eigenval matrix A. f) Given the basis for the eigenspace corresponding to eigenvalues λ = -2 and λ = 4-6 and matrix A are respectively. i) Is the matrix A diagonalizable? Give reason(s) for your answer. ii) If matrix A is diagonalizable, state the matrices P and D such that P-¹AP = D g) Without using a determinant method, give reason(s) why matrix A is invertible?

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.1: Introduction To Eigenvalues And Eigenvectors

Problem 35EQ

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