Question 15 Diagonalize the matrix A, if possible. That is, find an invertible matrix P and a diagonal matrix D such that A=PDP-1. -11 3-97 0-5 0 6 -3 4 A = P= 3 0, D= 1 0 -17 P= 5 3 0, D = 11 1 0 -1] P= 5 3 0 11 P = [1 5 -1 3 3 D= 0,D= [-5 0 0 1 00-2 0 0-5 0 0-5 0 0 01 0 0 0 150 OON

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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Question 15
Diagonalize the matrix A, if possible. That is, find an invertible matrix P and a diagonal matrix D such that A=PDP-1.
-11 3-97
0-5 0
6 -3 4
A =
O
O
P=
3 0, D=
1
0 -17
P= 5 3 0
11
1 0 -1]
P= 5 3 0
11
P =
[1 5 -1
3
3
D =
D=
0,D=
-5 0
0 1
01
0
00-2
0
0-5
0
0
0-5
0
DUO
0
NOO
0
150
OON
Transcribed Image Text:Question 15 Diagonalize the matrix A, if possible. That is, find an invertible matrix P and a diagonal matrix D such that A=PDP-1. -11 3-97 0-5 0 6 -3 4 A = O O P= 3 0, D= 1 0 -17 P= 5 3 0 11 1 0 -1] P= 5 3 0 11 P = [1 5 -1 3 3 D = D= 0,D= -5 0 0 1 01 0 00-2 0 0-5 0 0 0-5 0 DUO 0 NOO 0 150 OON
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