###### Exercise 5

Explain your responses to the following.

Why does Google use a Markov chain to compute the PageRank vector?

Describe two problems that can happen when Google constructs a Markov chain using the Google matrix \(G\text{.}\)

Describe how these problems are consistent with the Perron-Frobenius theorem.

Describe why the Perron-Frobenius theorem suggests creating a Markov chain using the modified Google matrix \(G' = \alpha G + (1-\alpha)H_n\text{.}\)