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Exercises 1 A square matrix is stochastic if the sum of the entries in each column is one. The Google matrix is computed by taking a combination

`G=\alpha **H+(1-\alpha )**S`

of two stochastic matrices. Show that G must be stochastic. 2 For this web of pages, the importance of each page should be equal. Verify it for

`\alpha =0.85`

. 3 [Bryan & Leise] Give the importance ranking for this web of pages. (a) Use

`\alpha =0.85`

. (b) Use

`\alpha =0.95`

. (c) Observe that while

`p_(3)`

is linked-to from all other pages, and therefore seems important, it is not the highest ranked page. What is the highest ranked page? Explain.