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an animal species that lived to a maximum of two years, using the transition matrix

[0.559 0.6 0.1

0 0

0.3 0

A= 0.7

0

The problem of determining the stable distribution for each age group can best be solved

using eigenvalues and eigenvectors.

a. What are the eigenvalues of A?

b. Determine an eigenvector corresponding to eigenvalue >= 1.

c. Determine an eigenvector corresponding to eigenvalue 2 = 1 that is physically

meaningful.

d. Determine a physically meaningful eigenvector corresponding to eigenvalue

2=1 where the sum of the entries is equal to 1.

e. Use the vector in part d) to determine the percentage of animal species that will

eventually have

current age zero.

current age one.

current age two.

f. Look at the plots you created for the population trends in Module 1 problems. Do

the trends match the eigen-analysis you just stepped through? How so?

Fig: 1