Hello, On this question I get eigenvalues of .07 and .11 from the quadratic equation, despite .07 and 0.11 not being the product of .77. Because the eigenvalues are so small, the subtraction (A-I lambda) is positive, such as .49. Because of this, there is only one negative to work with in the matrix, and the second column, second row index cannot be canceled out to zero using a multiple of the first row. Could point out what I'm doing wrong on the first part of this question? Thanks

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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Hello,

On this question I get eigenvalues of .07 and .11 from the quadratic equation, despite .07 and 0.11 not being the product of .77. Because the eigenvalues are so small, the subtraction (A-I lambda) is positive, such as .49. Because of this, there is only one negative to work with in the matrix, and the second column, second row index cannot be canceled out to zero using a multiple of the first row. Could point out what I'm doing wrong on the first part of this question?

Thanks

S. Denote the owl and tat population in
k (in months) by Xx=
aot time
particwar region
where Ok s the number of owls in the
re gu on, and Rk s the neumber of rats (in qhe thouwands). Supre
Okes- 0.60k +0.SRu and Ricay= p Ok+1.2Rk
Ok + 1.2Rk
a predwioh parameter.
claned form vector equation that models the owl and rat
where
is
a) Find
popwations for p=0.1.
6) Upadate your mobel goven that the iwtial population of owls s
400 and of Pats is 200 ,000.
c) Compute the lim Xx and explown what is happening long-term with
1-11 (A -.111)d= 3
+1 102
-1 109
the populations of owls and rats.
..1 1-2
[-1 1-09
1 1.021o
det (A-XI)= O
|.G-A S
- (.6-))(1.2 -) +05 = 0
:x -D\ +1.22
-.1 1.2-)
4.8±/3.24 - 4(4)(1.22)
1= 1.8 J3.24-4(. ?)
2(1)
1- 1-8±-1.64
A= 1-8 ±S.16
-X-18入.17-0
X=.09t .02
Transcribed Image Text:S. Denote the owl and tat population in k (in months) by Xx= aot time particwar region where Ok s the number of owls in the re gu on, and Rk s the neumber of rats (in qhe thouwands). Supre Okes- 0.60k +0.SRu and Ricay= p Ok+1.2Rk Ok + 1.2Rk a predwioh parameter. claned form vector equation that models the owl and rat where is a) Find popwations for p=0.1. 6) Upadate your mobel goven that the iwtial population of owls s 400 and of Pats is 200 ,000. c) Compute the lim Xx and explown what is happening long-term with 1-11 (A -.111)d= 3 +1 102 -1 109 the populations of owls and rats. ..1 1-2 [-1 1-09 1 1.021o det (A-XI)= O |.G-A S - (.6-))(1.2 -) +05 = 0 :x -D\ +1.22 -.1 1.2-) 4.8±/3.24 - 4(4)(1.22) 1= 1.8 J3.24-4(. ?) 2(1) 1- 1-8±-1.64 A= 1-8 ±S.16 -X-18入.17-0 X=.09t .02
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