Exercise 5.3.13

Answers

Considering the three states, large, intermediate-sized, and small car owners, the matrix is

(\begin{matrix} 0.7 & 0.1 & 0 \\ 0.3 & 0.7 & 0.1 \\ 0 & 0.2 & 0.9 \end{matrix})

and the initial vector is

P = (\begin{matrix} 0.4 \\ 0.2 \\ 0.4 \end{matrix}) .

So the vector in 1995 would be

A^{2} P = (\begin{matrix} 0.24 \\ 0.34 \\ 0.42 \end{matrix}) .

And the matrix $A$ is regular. So we may just find the fixed vector

(\begin{matrix} 0.1 \\ 0.3 \\ 0.6 \end{matrix}) .

jephianlin

2011-06-27 00:00