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
Chapter2: Matrices
Section2.1: Operations With Matrices
Problem 72E: Show that no 22 matrices A and B exist that satisfy the matrix equation. AB-BA=1001.
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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
A = 0-5 0
6-3 4
O
O
O
O
031
P= 5 3
P = 5 3
0
1
P = 0 3
Te
11 1
1 0 -1
[1 5
P= 5 3
13
0 D =
0
11 1
-1
[-5 0-2
D = 0-5 0
0-5 -2
3
D =
0, D=
1
-5 0
0-5 0
0 0-2
-5 0 0
0 1
0
00-2
-5
01
1
0-5 0
0 0-2
Transcribed Image Text: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 A = 0-5 0 6-3 4 O O O O 031 P= 5 3 P = 5 3 0 1 P = 0 3 Te 11 1 1 0 -1 [1 5 P= 5 3 13 0 D = 0 11 1 -1 [-5 0-2 D = 0-5 0 0-5 -2 3 D = 0, D= 1 -5 0 0-5 0 0 0-2 -5 0 0 0 1 0 00-2 -5 01 1 0-5 0 0 0-2
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