Let A be the PageRank transition matrix and let xk be a vector in the Markov chain with starting probability vector x0. Since n is very large, the direct multiplication xk+1 is computationally intensive. However, the computation can be simplified dramatically if we take advantage of the structured components of A given in equation (5). Because M is sparse. the multiplication Wk = MXk is compu(alionally much simpler. Show that if we set

Then
xk+1 = pwk + (1 - p)αke
where M,e and p are as defined in equation (5)

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e xk