5. (Markov Chain, 16pt) You want to analyze the surfing behavior on the following web-graph. There are seven web-pages, 1,2,3,4,5,6,7 and the links between them are as shown in the picture below (using applet at https://graphonline.ru/en/). a) [2pt] Build the corresponding adjacency matrix A: entry idi in A is 1 is there is a link from because there are links from 1 to 2 and 1 to 5 , but to no other page. Hint: there are 14 edges, so you should have 14 ones in your matrix. b) [4pt] We want to use A' as a transition matrix, but we cannot directly, since some columns of A add up to more than 1 , so A is not stochastic. Find a diagonal matrix D so that T=AD is a stochastic matrix (each column adds up to 1). State both D and T. Hint: A' is the transpose of A. To find D, scale each column of A' by the reciprocal of its sum. c) [3pt] Starting with page 1, compute the probabilities of being on any of the seven pages after 1 click, 5 clicks, 10 clicks and 100 clicks. Hint: Work with appropriate powers of T. Your answer will be 4 column vectors (one for each number of clicks) with probabilities