Chapter 9.3, Problem 34E

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.

$\begin{array}{l}\begin{array}{cccc}A& B& C& D\end{array}\\ P=\begin{array}{c}A\\ B\\ C\\ D\end{array}\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 1& 0& 0\\ .1& .1& .7& .1\\ .3& .1& .4& .2\end{array}\right]\end{array}$