Solution
= Solution
The <vector> $\delta_i-\pi$ has component sum zero, so part (c) applies to it. Part (b) gives $\pi^TP(t)=\pi^T$. Decompose $\delta_i^T=\pi^T+(\delta_i^T-\pi^T)$ to obtain
$$
\boxed{\delta_i^TP(t)=\pi^T+e^{-Rt}(\delta_i^T-\pi^T).}
$$
This is the full transition-law row, showing how the initial colour survives with exponentially decreasing weight.