 Solution

The vector ${\delta }_i-\pi$ has component sum zero, so part (c) applies to it. Part (b) gives ${\pi }^{T}P(t)={\pi }^T$. Decompose ${\delta }_i^T={\pi }^T+({\delta }_i^T-{\pi }^T)$ to obtainThis is the full transition-law row, showing how the initial colour survives with exponentially decreasing weight.