- (25 pts.)
Suppose there are three web pages,
*A*,*B*, and*C*, with the following links:*A*links to*B*and*C*.*B*links to*C*only.*C*links to*A*only.

Assuming no "taxation" of importance, find the PageRank of each page. Explain your reasoning; i.e., show the steps you take to solve the equations.

- (25 pts.)
Modify the links of Problem (1) by removing the link from
*C*to*A*. Using a 30% "tax" on importance, find the PageRank of each page. Explain your reasoning. - (25 pts.)
Now, modify the links of Problem (2) by adding a link from
*C*to itself. Repeat Problem (2). - (25 pts.)
For the pages of Problem (3), i.e., links
*A*->*B*,*A*->*C*,*B*->*C*, and*C*->*C*, find the hubbiness and authority of each page. Explain your work, including the matrices*A, A', AA'*, and*A'A*.