1550078481-Ordinary_Differential_Equations__Roberts_

362 Ordinary Differential Equations

THE HA.TRIX WHOSE EIGENVALUES AND EIGENVECTORS ARE TO BE CALCULATED IS

l .OOOOEtOO -2.0000EtOO

l.OOOOEtOO 3.0000EtOO

AN EIGENVALUE IS 2.00000EtOO t l.OOOOOEtOO I

THE ASSOCIATED EIGENVECTOR IS

-1.00000EtOO t -1.00000EtOO I

O.OOOOOEtOO t l.OOOOOEtOO I

AN EIGENVALUE IS 2.00000EtOO t -1.00000EtOO I

THE ASSOCIATED EIGENVECTOR IS

-1.00000EtOO t l .OOOOOEtOO I

O.OOOOOEtOO t -1.00000EtOO I

Figure 8.4 Complex Conjugate Eigenvalues and Eigenvectors

for Example 5.4.

EXERCISES 8.2

Use EIGEN or your computer software to compute the eigenval-

ues and associated eigenvectors of the following matrices.

1. (-~ -~) 2. (-3 -1)

2 -1

u

0

-i)

G

1

3. 1 4. 3 -1) -1
   0 -1 3 -1

5 (-1~

-1

-1~)

(l

(^1 1)
J
4 6.
(^1 1)
-2 1 -1 1 1
(^1 1)
7 (~
3 5
1:)
(~
3 5 2
!)
6 10 2 4 1
9 15 21
8. (^1 3 5)
18 30 42
5 2 4
4 1 3