a. Show that v1, v2, v3 are eigenvectors of A. b. Let x0 be any vector in

Question:

a. Show that v1, v2, v3 are eigenvectors of A.
b. Let x0 be any vector in R3 with nonnegative entries whose sum is 1. (In Section 4.9, x0 was called a probability vector.) Explain why there are constants c1, c2, c3 such that x0 = c1v1 = c2v2 + c3v3. Compute wr x0, and deduce that c1 = 1.
c. For k = 1, 2,..., define xk = Akx0, with x0 as in part (b). Show that xk †’ v1 as k increases.