Consider the following ridiculously simple linear system: (1 0 0 2) (x1 x2 ) = (1 1) . a. What is the solution of this linear system? You don't have to show your work. b. Set up a Neumann iteration with initial guess x0 = (0, 0)T . Calculate x1, x2, x3, and x4. Show your work. c. Based on your calculations in (b), what will xk equal for k > 0 when (i) k is odd and (ii) k is even? You don't have to show your work. d. Based on your answer to (c), does the Neumann iteration converge? e. Let M represent the matrix used in your Neumann iteration. Does M j 0 as j ? What does this tell you about the convergence of the Neumann iteration method? Is this consistent with your answer to (d)? Exercise 2. (Component Skill 4.2) For each linear system, decide whether Jacobi iteration is guaranteed or not guaranteed to con- verge to the solution. Justify each of your decisions in a sentence or two. a. 3 1 0 1 3 1 0 1 3 x1 x2 x3