Chapter 9.3, Problem 1ED

(A) For the initial-state matrix $S_0=\left[\begin{array}{ccc}a& b& c\end{array}\right]$, find the first four state matrices, $S_1,S_2,S_3$, and $S_4$, in the Markov chain with transition matrix

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

(B) Do the state matrices appear to be approaching a stationary matrix? Discuss.