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|

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.2: Direct Methods For Solving Linear Systems
Problem 1CEXP
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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
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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