Problem sheet M4B Lab - Math 6332 - Advanced Applications in Linear Algebra

Exercises M4B Lab - Due Friday, June 30, before midnight.

1. If sequence Ax, A³x, A'x,... represents populations from year to year, then write a

brief description about the population behavior for each of the following cases:

a. Stable:

b. Neutrally stable:

c. Unstable:

2. For each of the following population-transition matrices A determine if the process

defined by the sequence Ax, A²x, A'x.... is stable, neutrally stable, or unstable. Record

your findings next to matrix. Explain your conclusions.

[0.559 0.63 0.1]

0 0

0.3 0

0.21 0.64 0.12

b. A = 0.69 0 0

0

0.36 0

a.

A= 0.7

0

0.868 0.4 0.2

0 0

0.2 0

c. A= 0.3

0

[0.5

3. For the population transition matrix A=

1

0

0.44 0.06]

0

0

1

0

[14]

for the initial population vector x = 20 (in millions) that

11

[15.807

lim 4*x=u= 15.807

15.807]

How is u related to the eigenvectors of A? Be specific.

it was determined directly