Let $G=([4], E)$ be the directed graph associated with matrix $P$ in the above exercise. Suppose that $G$ is the graph associated with four webpages. Let $P^{W}$ be the associated transition matrix for the random walk on this graph (webpages). (a) Write down $P^{W}$. Is $P^{W}$ ergodic? (b) Consider the associated random walk with reset, i.e., the Markov chain with the transition matrix $P=(1-\alpha) P^{W} \alpha J$ where $J=\frac{1}{4} \mathbf{1 1}{ }^{T}$ and the reset probability $\alpha=0.1$. Find the ranking of the four webpage (states) using the page-rank algorithm