A rail authority models the monthly change in commuters’ usual station between North (N) and South (S). The state matrix is a column matrix, with entries giving the proportions using N and S, in that order. The transition matrix is

$$T=\begin{pmatrix}0.8&0.3\\0.2&0.7\end{pmatrix},$$

where rows represent the station used in the next month and columns represent the station used in the current month. Initially,

$$s_0=\begin{pmatrix}0.10\\0.90\end{pmatrix}.$$