) Suppose that the matrix A has the following eigenvalues and eigenvectors:51 = -1+5i with v1-4 – 4iand5d2 = -1– 5i with vz = :-4+ 4i%3|Write the general real solution for the linear system i' = AF, in the following forms:A. n eigenvalue/eigenvector form:Inx(t)y(t)t= C1e+ c2eB. In fundamental matrix form:¤(t)'y(t)C1C. As two equations: (write "c1" and "c2" for c and c2 )r(t) =y(t)=+

Answered: Image /qna-images/answer/9dd146b2-4bed-4f33-8602-8dc30f5c1afc.jpg

) Suppose that the matrix A has the following eigenvalues and eigenvectors: 1= -1+ 5i with v 5 %3D -4 – 4i e = -1- 5i with ö2 -4+ 4i e the general real solution for the linear system 7' = AF, in the following forms: eigenvalue/eigenvector form: ¤(t) + C2 fundamental matrix form: y(t) s two equations: (write "c1" and "c2" for c and c2 ) r(t) = y(t):

) Suppose that the matrix A has the following eigenvalues and eigenvectors: 1= -1+ 5i with v 5 %3D -4 – 4i e = -1- 5i with ö2 -4+ 4i e the general real solution for the linear system 7' = AF, in the following forms: eigenvalue/eigenvector form: ¤(t) + C2 fundamental matrix form: y(t) s two equations: (write "c1" and "c2" for c and c2 ) r(t) = y(t):

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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Question

) Suppose that the matrix A has the following eigenvalues and eigenvectors:
5
1 = -1+5i with v1
-4 – 4i
and
5
d2 = -1– 5i with vz = :
-4+ 4i
%3|
Write the general real solution for the linear system i' = AF, in the following forms:
A. n eigenvalue/eigenvector form:
In
x(t)
y(t)
t
= C1
e
+ c2
e
B. In fundamental matrix form:
¤(t)'
y(t)
C1
C. As two equations: (write "c1" and "c2" for c and c2 )
r(t) =
y(t)
=
+

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