A diagonalization of the matrix A is given in the form P-1AP = D. List the eigenvalues of A and bases for the corresponding eigenspaces. (Repeated eigenvalues should be entered repeatedly with the same eigenspaces.) 21 =-1 10 2 2 2 001 2 2 1 181235 107225 101225 5 1 0 1 -1 1 = 4 0-1 40 0 0 0 0 0 0 -1 (smallest 2-value) -A has eigenspace span 0 |1 | -1 具首 0 (1) 22 = 0 has eigenspace span -1 1 -1 -> 13 = 4 has eigenspace span 0 (largest A-value) ↓ ↑
A diagonalization of the matrix A is given in the form P-1AP = D. List the eigenvalues of A and bases for the corresponding eigenspaces. (Repeated eigenvalues should be entered repeatedly with the same eigenspaces.) 21 =-1 10 2 2 2 001 2 2 1 181235 107225 101225 5 1 0 1 -1 1 = 4 0-1 40 0 0 0 0 0 0 -1 (smallest 2-value) -A has eigenspace span 0 |1 | -1 具首 0 (1) 22 = 0 has eigenspace span -1 1 -1 -> 13 = 4 has eigenspace span 0 (largest A-value) ↓ ↑
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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Transcribed Image Text:A diagonalization of the matrix A is given in the form P-1AP = D. List the eigenvalues of A and bases for the corresponding eigenspaces. (Repeated eigenvalues should be entered repeatedly with the same eigenspaces.)
21
=-1
10
2 2 2
001
2 2 1
181235
107225
101225
5
1
0
1 -1
1
=
4
0-1
40
0
0 0 0
0 0 -1
(smallest 2-value)
-A
has eigenspace span
0
|1
| -1
具首
0
(1)
22 = 0
has eigenspace span
-1
1
-1
->
13 = 4
has eigenspace span
0
(largest A-value)
↓ ↑
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