Chapter 9.3, Problem 29E

In Problems 29-34, find the limiting matrix for the indicated standard form. Find the long-run probability of going from each nonabsorbing state to each absorbing state and the average number of trials needed to go from each nonabsorbing state to an absorbing state.

$\begin{array}{l}\begin{array}{ccc}A& B& C\end{array}\\ P=\begin{array}{c}A\\ B\\ C\end{array}\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ .1& .4& .5\end{array}\right]\end{array}$