formula

$\begin{pmatrix} P_A(i+1) \\ P_B(i+1) \\ P_C(i+1) \\ P_D(i+1) \\ P_E(i+1) \\ \end{pmatrix} = \begin{pmatrix}\frac{3}{8} & \frac{3}{8} & 1 & \frac{1}{2} & 1\\\frac{3}{8} & 0 & 0 & \frac{1}{2} & 0\\0 & \frac{3}{8} & 0 & 0 & 0\\\frac{1}{4} & 0 & 0 & 0 & 0\\0 & \frac{1}{4} & 0 & 0 & 0\end{pmatrix} \begin{pmatrix} P_A(i) \\ P_B(i) \\ P_C(i) \\ P_D(i) \\ P_E(i) \\ \end{pmatrix}$