Chapter 9, Problem 23RE

In Problems 22 and 23, determine the long-run behavior of the successive state matrices for the indicated transition matrix and initial-state matrices.

$\begin{array}{l}\begin{array}{ccc}A& B& C\end{array}\\ P=\begin{array}{c}A\\ B\\ C\end{array}\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ .2& .6& .2\end{array}\right]\\ \left(\text{A}\right)S_0=\left[\begin{array}{ccc}0& 0& 1\end{array}\right]\\ \left(\text{B}\right)S_0=\left[\begin{array}{ccc}.5& .3& .2\end{array}\right]\end{array}$