Problem#1 Gauss Elimination" A set of linear equations are given below. u+2v + 2w = 3, 4u + 41, + 2w = 6, Write a matrix in the form A X - B where X - [u v w In Gaussian elimination method an augmented matrix Aa- [A B] is reduced into upper triangular matrix using a series of row operations. Here X and B are column vectors. Write a MATLAB script and solve for the unknown variables u, v and w using Gaussian elimination and "back-substitution" method. In the class yesterday, you learned about (Ei, Ez. Es) elementary row operation matrices that will perform scaling operation, interchange of rows, and a combination operation called replacement operation. Develop appropriate row operation matrices to implement Gaussian elimination method with MATLAB. Note you may combine two elementary operation matrices Esv and Ee into a single row operation matrix M = E,' Es. An algorithm for implementing "back-substitution" method is given below: Algorithm Back-Substitution for Upper Triangular System loop backwards over columns (stop if matrix is singular ) for j = n to 1 if ujj 0 then stop for i = 1 to j-1 end compute solution component ) ( update right-hand side ) end