Can someone help me with part b and c? Please answer in details for part b.

(30 points) Consider a linear system An: = b, where A E RM" and x,b E R\". We denote the diagonal part of A as a new matrix D, an 0 g p: 9\".\" 9 , 0 0 am and assume that D is non-singular. Consider the following iterative scheme. Given an arbitrary initial vector 3(0) E IR", N\") = G(a:) :2 (I D\"A)za;(") + 13-11;, I: = 0,1,2,. . . . I 6 RM" is the identity matrix. (a) Show that G : 1R\" > R" is a fixed-point operator. and the fixed-point solution solves the linear system Ax = b. (b) Compute the number of floating-point operations (flops) for each iteration of the fixed-point method. When is this iterative scheme preferred to the LU factorization for solving a linear system Ax = b based on the computational complexity? (c) If laggl > Z [av-L which holds forz' = 1,2, . . . ,n. showthat R:=||D'1AI||