Problem. A ais a Vandermonde matrix of order 5 where aand b 1,2,3,4,5. Use the following pseudocode to find the solution of ATand print L and U for the LU-factorization of A. Also in the same output double check the solution of A = by corresponding M LAB commands. Explain steps by commenting on them. Algorithm Gaussian-Elimination Input: A and b Output: the solution of A = b : L and U for the LU n of A n = length of 6.= zero (column) vector of order n, L = the identity matrix of order n for k 1 to (n 1) for i-k+1 to n for j = k + 1 to n b(i) b)-mb(k) U A fori 1 to n for j 1 to i-1 U(i,j) = 0: (n)-bn)/A(n, for i = n _ 1 to 1 sum =b(i); for j-i1 to sum = sum-A(i, j) * r(j); (6)-sum/AG,i) return r, L, U Useful MATLAB commands: (See Matlab 0) A = fliplr(vander(1 : 1 : 5)) * To find solution of Al-b: A\b