Chapter 9.1, Problem 21E

In Problems 21-26, use the transition matrix

$\begin{array}{l}\begin{array}{ccc}A& B& C\end{array}\\ P=\begin{array}{c}A\\ B\\ C\end{array}\left[\begin{array}{ccc}.2& .4& .4\\ .7& .2& .1\\ .5& .3& .2\end{array}\right]\end{array}$

to find $S_1$ and $S_2$ for the indicated initial state matrix $S_0$.

$S_0=\left[\begin{array}{ccc}0& 1& 0\end{array}\right]$