Chapter 9.3, Problem 37E

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 31 with

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