Numerical Methods question; please upload part answers if full question is not completed

2. Consider the linear system Ax = b, where A is a square non-singular matrix with non-zero diagonal elements. To solve this linear system, consider the following iterative method: given x(0), for k 2 0, compute x(*+?) such that LAX(*+) = b - (A - LA)X(*), compute x(*+1) = wx(k+!) + (1 -w)x(#) where w E R is a real parameter, and LA is the lower triangular part of A including the diagonal. (a) Show that this iterative method can be rewritten in the form x ( 4+1) = Bux(*) +f, where By = ((1 - w)I - WLA'(A - LA)) and fu = why'b. [6] (b) Consider now A = and b = Compute the first iterate x(1) taking x(0) = (1, 1) and arbitrary w. [4] (c) Determine for which values of the parameter w the proposed iterative method is convergent considering A and b as in the previous question. [5]