Problem 1.4 (a) Let A, B = B* " he two stochastic matrices. Show that A - B is a stochastic matrix. ib) Let A, B = R he two stochastic matrices. Let A= (0,1). Show that A- 4 + (1 - A)- B 15 a stochastic matrix. (c) Let A= R* be a stochastic matrix. Show that the vector v = B defined by (v, 1 for i = 1,....n is an eigenvector of 4. Compute the corresponding eigenvalue. (g; is the i-th standard unit vector. This is a column-vector with a +1 in th i-th entry; all other entries are (1)