27. Find the characteristic equation, eigenvalues, eigenvectors and the bases for the eigenspaces of the following matrices. For each eigenvalue also find the rank of Al – A: a)A = 3 1 0 0 -1 1 -1 .1 -1 0] 1 b)A

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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27. Find the characteristic equation, eigenvalues, eigenvectors and the bases for the eigenspaces
of the following matrices. For each eigenvalue also find the rank of 11 – A:
a)A = ;
[3 1
0 0
-1 1 -1
li -1 0
1
b)A
[1 -1 -2]
c) A = |-1 2 5
0 1 3
Transcribed Image Text:27. Find the characteristic equation, eigenvalues, eigenvectors and the bases for the eigenspaces of the following matrices. For each eigenvalue also find the rank of 11 – A: a)A = ; [3 1 0 0 -1 1 -1 li -1 0 1 b)A [1 -1 -2] c) A = |-1 2 5 0 1 3
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