A campus club records which of two cafés its members visit each Friday. The transition diagram in Figure 1 gives the probabilities that a member visits each café on the next Friday, based on the café visited this Friday.

Let $s_n$ be the column state matrix after $n$ weekly transitions, using the state order North, South. On the Friday of the survey, the state matrix is

$$s_0=\begin{pmatrix}0.75\\0.25\end{pmatrix}.$$