4. (38 points) Consider the linear system Ax b where the entries of A are defined by 2i, when j = i and i = 1, 2,...,n, Sj= i + 2 and i = 1,2,...,n - 2 0.5i, when j=i-2 and i = 3, 4, ..., n dij (j=i+4 and i=1,2,...,n - 4 0.25i, when lj=i - 4 and i = 5, 6, ..., n 0, otherwise. and b= (* 1 #)". Suppose n = 20,000. (a) Using MATLAB (or any other programming language), implement the Gaussian elimination (without pivoting strategies) to obtain a solution to the linear system. You may modify from the code provided in the lecture. You should take note of the special structure of the coefficient matrix to reduce computational cost. Report the runtime needed and the first 10 entries of the solution up to 8 decimal places. (b) i. Deduce a formula for updating the (k +1)-th iterates ** (6+1) of SOR method, for entries i = 1, ..., n. ii. Hence, using MATLAB (or any other programming language), im- plement the SOR method for solving the linear system approximately with relaxation parameter w = 1.2. Start with initial guess Xo = 0 and use the stopping condition max {|AXk+1 bl}