Consider the linear system y' (t) = Ay(t) where the real matrix A has an [2²4] · eigenvalue X = −1+i with associated eigenvector v = [y₁ (t)] Assume your real solution is in the form (t)e where
Consider the linear system y' (t) = Ay(t) where the real matrix A has an [2²4] · eigenvalue X = −1+i with associated eigenvector v = [y₁ (t)] Assume your real solution is in the form (t)e where
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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The options for matching the values of c1 and c2 are -4 through 1.
![Consider the linear system y' (t) = Ay(t) where the real matrix A has an
[2²4]
eigenvalue X = −1+i with associated eigenvector v =
Assume your real solution is in the form
cos(t)
2 cos(t) + sin(t)
Match a and b to the correct values
a = [c1]
and
b = [c2].
y(t) = e-t
=e-¹ [20
y₁ (t)]
Y₂ (t).
=
(t)c where
a sin(t)
(bcos(t)) + 2 sin(t).
6)].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fef258a66-0367-4e84-ab3e-34166dbe87ca%2Fd0392053-6c7d-4e80-aac4-02ee033cf55a%2Fptx6wq_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the linear system y' (t) = Ay(t) where the real matrix A has an
[2²4]
eigenvalue X = −1+i with associated eigenvector v =
Assume your real solution is in the form
cos(t)
2 cos(t) + sin(t)
Match a and b to the correct values
a = [c1]
and
b = [c2].
y(t) = e-t
=e-¹ [20
y₁ (t)]
Y₂ (t).
=
(t)c where
a sin(t)
(bcos(t)) + 2 sin(t).
6)].
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