\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}
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