B3: Consider the matrix: 1 3 A = -2 -3 -3 2 -1 -1 a) Find the eigenvalues of A. For each eigenvalue A, find the dimension of the eigenspace ker(A – AI) and give a basis (i.e. find eigenvectors). You are given that (A - 2)(12 +6A +8) = + 4x2 - 4A- 16. b) Decide if A is diagonalisable. If it is, then write A as: A = PDP-, where D is a diagonal matrix. c) Compute A".

B3: Consider the matrix: 1 3 A = -2 -3 -3 2 -1 -1 a) Find the eigenvalues of A. For each eigenvalue A, find the dimension of the eigenspace ker(A – AI) and give a basis (i.e. find eigenvectors). You are given that (A - 2)(12 +6A +8) = + 4x2 - 4A- 16. b) Decide if A is diagonalisable. If it is, then write A as: A = PDP-, where D is a diagonal matrix. c) Compute A".

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 36EQ: Consider again the matrix A in Exercise 35. Give conditions on a, b, c, and d such that A has two...

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