MATH 551 Final: MATH 551 KSU Sample1FinalSolution s07
15 Feb 2019
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Final test: sample 1 with solutions (250 points) Problem 1 (30 points) a web of 5 pages is described by a directed graph whose matrix is given by. Do the following (10 points each): draw the web and its backlinks. Solution: this is easy to do: just remember how a matrix describes a directed graph. For instance, since the element a(1, 3) equals 1, then there is an arrow (backlink) going from page 1 to page 3. Since a(4, 1) = 0, then there is no backlink going from page 4 to page 1, and so on: find the importance score matrix b for the web. Solution: once the web is understood, the importance scores x1, . , x5 verify the fol- lowing x1 = x2 = x3 = In matrix notation, we obtain x1 x2 x3 x4 x5. Notice that all the columns of b add up to 1 (that is, b is column stochastic).
