For the system X' = AX, if the characteristic polynomial for the 3x3 matrix A is 1 given by P(r) = [- (r –1)’]. If A-I= 1 then the fundamental matrix 1 1 2 -2 eAt is e' +te te te' a) te' e' +te' te - 2te - 2te e' - 2te' e e' e b) e te te' e' te' te [te te' te c) te te te te te te e' + te te' d) te te e te'

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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For the system X' = AX, if the characteristic polynomial for the 3x3 matrix A is
1
1
given by P(r) = [- (r –1)’]. If A–I= 1
then the fundamental matrix
1
1
-2 -2
- 2
e At is
[e'+te'
te'
te'
a)
te'
e' +te'
te
- 2te
- 2te'
e' - 2te'
e
e'
e'
b) e' te' te'
e' te' te'
te' te' te
c) te' te' te'
te' te' te
e' + te
te'
d)
te
te'
e'
te'
Transcribed Image Text:For the system X' = AX, if the characteristic polynomial for the 3x3 matrix A is 1 1 given by P(r) = [- (r –1)’]. If A–I= 1 then the fundamental matrix 1 1 -2 -2 - 2 e At is [e'+te' te' te' a) te' e' +te' te - 2te - 2te' e' - 2te' e e' e' b) e' te' te' e' te' te' te' te' te c) te' te' te' te' te' te e' + te te' d) te te' e' te'
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