Chapter 9.1, Problem 9E

To determine

To calculate : The value of the first-state matrix $S_1$ for the initial-state matrix $S_0=\left[\begin{array}{cc}1& 0\end{array}\right]$, and interpret it with a tree diagram given that the transition matrix is $\begin{array}{l}\text{ A B}\\ P=\begin{array}{c}\text{A}\\ \text{B}\end{array}\left[\begin{array}{cc}0.8& 0.2\\ 0.4& 0.6\end{array}\right]\end{array}$.