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 i,j in A is 1 is there is a link frompage i to page j (a directed arrow in the picture).Hint: the first row of A is [0 1 0 1 1 0 1], because there are links from 1 to 2, 4, 5, and 7 and no links to 1, 3, and 6.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 ofA' add up to more than 1, so A' is not stochastic. Find a diagonal matrix D so that T = A' * D is a stochastic matrix (each column adds up to 1). State both D and T.Hint: A' is the transpose ofA. To find D, scale each columnof A' by the reciprocal of its sum.

c) [3pt] Starting with page 2, compute the probabilities of being on any of the pages after 1 click,5, 10 clicks and 100 clicks.Hint: Work with appropriate powers of T. Your answer will be 4column vectors with probabilities.

d) [3pt] Redopart c) but starting with page 4. How do the results differ? Do they differ?