Let G = (V, E) with V= {1,...,n} and E = {21,...,n 1}. This is called a (directed) star graph and is shown below for n = 5. Answer the following questions. (25 regular points in total) Note: The n = 5 picture is just an example, so your answers should be for general n. A. What do you expect the hub and authority scores to be? Why? B. Let A be the adjacency matrix of G. Find length-n vectors x and y such that A = xy, and compute AAT in terms of x and y. C. Using your answer to Part B, prove that .x is an eigenvector of A AT. What is the associated eigenvalue? (Your answer should be in terms of n.) D. Prove that all other eigenvalues of A AT are zero. E. Using your answers above, what are the hub and authority scores? Justify your answer. Is this what you expected in Part A? 5 2