Suppose the hyperlink matrix of a directed graph is given as follows:
$$A = \begin{pmatrix}0&0&\frac{1}{3}&\frac{1}{2}&0\\ \:\:\:0&0&0&\frac{1}{2}&\frac{1}{3}\\ \:\:\:0&\frac{1}{2}&0&0&\frac{1}{3}\\ \:\:\:\frac{1}{2}&0&\frac{1}{3}&0&\frac{1}{3}\\ \:\:\:\frac{1}{2}&\frac{1}{2}&\frac{1}{3}&0&0\end{pmatrix}$$
How to find the PageRank of the highest rank page?
I started with the initial vector as $x =(\frac{1}{5},\frac{1}{5},\frac{1}{5},\frac{1}{5},\frac{1}{5})$ and then started the iterative process finding $Ax,A^2x.$