Chapter 9.3, Problem 39E

Problems 35-40 refer to the matrices in Problems 29-34. Use the limiting matrix $P$ found for each transition matrix $P$ in Problems 29-34 to determine the long-run behavior of the successive state matrices for the indicated initial-state matrices.

For matrix $P$ from Problem 33 with

$\begin{array}{l}\left(\text{A}\right)S_0=\left[\begin{array}{cccc}0& 0& 0& 1\end{array}\right]\left(\text{B}\right)S_0=\left[\begin{array}{cccc}0& 0& 1& 0\end{array}\right]\\ \left(\text{C}\right)S_0=\left[\begin{array}{cccc}0& 0& .4& .6\end{array}\right]\left(\text{D}\right)S_0=\left[\begin{array}{cccc}.1& .2& .3& .4\end{array}\right]\end{array}$