Chapter 8.1, Problem 47E

(a)

To determine

To calculate: The distribution matrices for next four generations for the provided stochastic matrix $A=\left[\begin{array}{cc}.1& .6\\ .9& .4\end{array}\right]$ and the initial distribution matrix ${\left[\begin{array}{c}.5\\ .5\end{array}\right]}_0$.

(b)

To determine

To calculate: The value of $A^{4}B$ and compare the value with the obtained result in part (a) for the provided stochastic matrix $A=\left[\begin{array}{cc}.1& .6\\ .9& .4\end{array}\right]$ and the initial distribution matrix ${\left[\begin{array}{c}.5\\ .5\end{array}\right]}_0$.