4) The matrix exponential e4t is e5t +e-t e5t – e-t' 0.5 e5t e-t est +e-t e5t – e-t e5t +e-t' 0.5 e5t – e-t est +e-t [ ešt +et eõt – e-t] 0.5 ešt +e-t e5t +e-t. ešt + e-t e5t +e-t 0.5 | ešt + e-t ešt +e-t|
4) The matrix exponential e4t is e5t +e-t e5t – e-t' 0.5 e5t e-t est +e-t e5t – e-t e5t +e-t' 0.5 e5t – e-t est +e-t [ ešt +et eõt – e-t] 0.5 ešt +e-t e5t +e-t. ešt + e-t e5t +e-t 0.5 | ešt + e-t ešt +e-t|
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Q4 only
![Solve Q4 only
Consider the system of equations below:
dx
2x + 3y
dt
dy
3x + 2y
dt
If we denote Vi and V2 as the eigenvectors corresponding to A1 and A2,
matrix H = [V V2]
3) The Jordan matrix J = H-'AH is given by
4) The matrix exponential eAt is
ešt +e-t est – e-t
0.5
est
e-t est +e-t]
e5t – e-t e5t +e-t
0.5
e5t – e-t est +e-t,
e5t +et ešt – et
0.5
e5t +et est +e-t
e5t +e-t e5t +e-t
0.5
e5t +e-t ešt +e=t](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F557b876d-7aac-4061-bb42-34689ab8cb9b%2F5b846c2d-004f-41c6-9528-6f2f0af96a26%2Fyc451vl_processed.png&w=3840&q=75)
Transcribed Image Text:Solve Q4 only
Consider the system of equations below:
dx
2x + 3y
dt
dy
3x + 2y
dt
If we denote Vi and V2 as the eigenvectors corresponding to A1 and A2,
matrix H = [V V2]
3) The Jordan matrix J = H-'AH is given by
4) The matrix exponential eAt is
ešt +e-t est – e-t
0.5
est
e-t est +e-t]
e5t – e-t e5t +e-t
0.5
e5t – e-t est +e-t,
e5t +et ešt – et
0.5
e5t +et est +e-t
e5t +e-t e5t +e-t
0.5
e5t +e-t ešt +e=t
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