Let A be a 3 x 3 diagonalizable matrix with eigenvalues: À, = -1 withcorresponding eigenvector v, =and 2, = 2 with correspondingeigenvectors vz = 0 and vz =2 . Then P1 AP = D with:[-1 -5D =|-2-1 0 0]D =|02 0 and2 and21-1.[-5P =|00 012[-12 0O 21P =|0-2-1 -1]the above D and Pthe above D and P[2 0D = 0 2Lo o[-5P =|00 and12-2-12None of thesethe above D and P

Introduction: A square matrix is diagonalizable. Diagonalization is the process where the matrix A…

Let A be a 3 x 3 diagonalizable matrix with eigenvalues: À, = -1 with corresponding eigenvector v, = and d2 = 2 with corresponding eigenvectors v, =|0 and vy = 2 . Then P1 AP = D with: -1 -5 D =|-2 [-1 0 0] 2 0 and O 2] 1 2 D =| 0 2 and -1 2 1 [-1 0 01 2 0 0 0 21 [-5 P =|0 -2 -1] P =|0 -1 the above D and P the above D and P [2 0 D = 0 2 Lo o -1 2 0 and [-5 P =|0 1 2 -2 1 -1 2

Let A be a 3 x 3 diagonalizable matrix with eigenvalues: À, = -1 with corresponding eigenvector v, = and d2 = 2 with corresponding eigenvectors v, =|0 and vy = 2 . Then P1 AP = D with: -1 -5 D =|-2 [-1 0 0] 2 0 and O 2] 1 2 D =| 0 2 and -1 2 1 [-1 0 01 2 0 0 0 21 [-5 P =|0 -2 -1] P =|0 -1 the above D and P the above D and P [2 0 D = 0 2 Lo o -1 2 0 and [-5 P =|0 1 2 -2 1 -1 2

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section: Chapter Questions

Problem 12RQ

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