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
Suppose that the matrix A has the following eigenvalues and eigenvectors:
Transcribed Image Text:= 2i with v1
-4 + 5i
and
= -2i with v2
-4 – 5i
Write the general real solution for the linear system r' = Ar, in the following forms:
A. In eigenvalue/eigenvector form:
1
x(t)
-5
= C1
y(t)
e
-4
t
+ C2
+
e
B. In fundamental matrix form:
x(t)
C1
C. As two equations: (write "c1" and "c2" for c1 and c2 )
x(t) =
y(t) =
LO
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