Question 17Diagonalize the matrix A, if possible. That is, find an invertible matrix P and a diagonal matrix D such that A=PDP-1.[-11 3 -9A = 0-5 06-3 4OOOO031P= 5 3P = 5 301P = 0 3Te11 11 0 -1[1 5P= 5 3130 D =011 1-1[-5 0-2D = 0-5 00-5 -23D =0, D=1-5 00-5 00 0-2-5 0 00 1000-2-50110-5 00 0-2

Answered: Image /qna-images/answer/7a78aba9-941a-4b9f-85ae-82d61019adbe.jpg

Question 17 Diagonalize the matrix A, if possible. That is, find an invertible matrix P and a diagonal matrix D such that A=PDP-1. [-11 3 -9] 0-50 6 -3 4 A = P= 5 3 1 P = 1 0 -1 P= 5 3 P = 1 0 -1 1 — om 0, D = 1 3 1 1 1 0, D = 0, D= 1 [1 5 -1] 3 0 D = 3 13 1 -5 0-50 0-5 T-5 0 0 0 0-2 0-5 ܘ ܘ -5 ܘ ܘ ܟ NON 01 00-2 -5 0 0-5 0 0 0-2

Question 17 Diagonalize the matrix A, if possible. That is, find an invertible matrix P and a diagonal matrix D such that A=PDP-1. [-11 3 -9] 0-50 6 -3 4 A = P= 5 3 1 P = 1 0 -1 P= 5 3 P = 1 0 -1 1 — om 0, D = 1 3 1 1 1 0, D = 0, D= 1 [1 5 -1] 3 0 D = 3 13 1 -5 0-50 0-5 T-5 0 0 0 0-2 0-5 ܘ ܘ -5 ܘ ܘ ܟ NON 01 00-2 -5 0 0-5 0 0 0-2

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter7: Eigenvalues And Eigenvectors

Section7.CR: Review Exercises

Problem 64CR: a Find a symmetric matrix B such that B2=A for A=[2112] b Generalize the result of part a by proving...

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