This preview shows page 1. Sign up to view the full content.
ENME 361 Fall 2008
Solution for Quiz #9
(November 20, 2008; Duration: 10 minutes)
1)
Consider the following system of algebraic equations:
2
11
11
1
11
12
2
21
21
22
1
22
0
X
km
k
X
kk
m
λ
⎡⎤
−−
⎧⎫
=
⎨⎬
⎢⎥
⎩⎭
⎣⎦
i)
Define eigenvalues.
Solution
:
Eigenvalues are the special values of
2
, for which
X
11
and
X
21
are nonzero or not trivial.
ii) Determine the characteristic equation for this system.
Solution
:
The characteristic equation is given by
2
11
11
12
2
21
22
22
det
0
k
m
=
which when expanded leads to
22
11
11
22
22
12
21
()
(
)
0
k
k
λλ
−
=
.
ii)
Say, the determined eigenvalues are
λ
1
and
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 02/13/2011 for the course ENME 361 taught by Professor Yoo during the Spring '11 term at Maryland.
 Spring '11
 yoo

Click to edit the document details