Matrix (2 1 0' A = |1 2 0 0 0 1/ satisfies the property C 'AC = D where C and D are, respectively, an orthogonal matrix and a diagonal matrix. So C and D can be: (–1/v2 1/v2 o' O C= 1//2 1/v2 0 0 0 1, 1 0 0 y D=|0 3 0 0 0 ( 1/v/2 1//2 O C=| 1/v2 -1//2 0 1. 00 y D= 0 30 1 0 0 1 -1/v2 1/v2 0 1 0 0 y D=0 1 o O C- 1//2 1//2 0 0 0 3 (–1/v2 1/v2 o 300 O C= 1//2 1//2 0 y D= 0 1 0 0 1

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Matrix
(2 1 0'
A = |1 2 0
0 0 1/
satisfies the property
C 'AC = D where C and D are, respectively, an orthogonal matrix
and a diagonal matrix. So C and D can be:
(–1/v2 1/v2 o'
O C=
1//2 1/v2 0
0 0 1,
1 0 0
y D=|0 3 0
0 0
(1/v/2 1//2
O C=| 1/v2 -1//2 0
1.
00
y D=
0 30
1
0 0 1
-1/v2 1/v2 0
1 0 0
y D=0 1 o
O C-
1//2 1//2 0
0 0 3
(–1/v2 1/v2 o
300
O C=
1//2 1//2 0
y D=
0 1
0 0 1
Transcribed Image Text:Matrix (2 1 0' A = |1 2 0 0 0 1/ satisfies the property C 'AC = D where C and D are, respectively, an orthogonal matrix and a diagonal matrix. So C and D can be: (–1/v2 1/v2 o' O C= 1//2 1/v2 0 0 0 1, 1 0 0 y D=|0 3 0 0 0 (1/v/2 1//2 O C=| 1/v2 -1//2 0 1. 00 y D= 0 30 1 0 0 1 -1/v2 1/v2 0 1 0 0 y D=0 1 o O C- 1//2 1//2 0 0 0 3 (–1/v2 1/v2 o 300 O C= 1//2 1//2 0 y D= 0 1 0 0 1
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