1 3 0 4 2 0 0 6. -2 1 0 1 0 0

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question

a). Find a basis for each eignspase.

b). Write eignspace as the span of it's basis vector

Sh
1 3
0 4
0 0
0 0
2
5
Find the eigenvalues for
6
2 = 1 with multiplicity of 2, 1 = -2, 1= 4
-2 1
0 1
Sh
1
Eigenvectors for 2 = 1:
Sh
1
-1
Eigenvectors for 2 = -2:
3
Sh
1
1
Eigenvectors for 2 = 4:
ㅇ
ㅇ
1 3
0 4
The eigenvectors for
0 -2 1
0 0
1
1
1
1
3
Transcribed Image Text:Sh 1 3 0 4 0 0 0 0 2 5 Find the eigenvalues for 6 2 = 1 with multiplicity of 2, 1 = -2, 1= 4 -2 1 0 1 Sh 1 Eigenvectors for 2 = 1: Sh 1 -1 Eigenvectors for 2 = -2: 3 Sh 1 1 Eigenvectors for 2 = 4: ㅇ ㅇ 1 3 0 4 The eigenvectors for 0 -2 1 0 0 1 1 1 1 3
1
3
0 4
A =
2
6.
-2 1
0 0 0 1
Transcribed Image Text:1 3 0 4 A = 2 6. -2 1 0 0 0 1
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