Use a transition matrix to predict the next step
A weekly survey records which shop each customer chooses. The following data give the current state and the one-step transition rule
The matrix state order is Riverside and Market Square. Columns represent the current state and rows represent the state next week. An entry is the proportion currently in its column state that will be in its row state next week
\[T = \begin{bmatrix} 0.55 & 0.45 \\ 0.45 & 0.55 \end{bmatrix}\]
The current-state column uses the same state order. Its entries are counts of customers
\[S_{\mathrm{now}} = \begin{bmatrix} 140 \\ 60 \end{bmatrix}\]