Explain your responses to the following.

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

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

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

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