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MATLAB CHALLENGE PROBLEM 1 Gaussian Elimination Program Gaussian Elimination can be a valuable tool for quickly solving large systems of linear equations. While its application is primarily limited to systems with equal numbers of equations and unknowns (i.e. they produce square coefficient matrices), and there are certainly more computationally efficient algorithms available, Gaussian Elimination provides a fairly straight-forward procedure that can be easy to follow For this Challenge Problem, your task is to write a well-structured MATLAB program to perform Gaussian Elimination with full pivoting. Your program should have the following attributes: Receive a square [n n] matrix and a corresponding [n 1] or [1 n] vector of constants as o If the matrix is not square, the program should terminate with an error message o Similarly, if the matrix is singular (i.e. its determinant is equal to zero), a similar error its primary input arguments. specifying that the function requires a square matrix. message should be returned, and the program terminated. If the constants vector does not have the same number of entries as the number of rows in the matrix, an error message should be created and the program terminated. o .Return both the upper-triangular matrix created using Forward Elimination, and the column vector of the solutions The program should be fully-commented with headers, sections, and explanations of what each section of code is trying to accomplish. Once your code is written, use your new function to solve the following problem (adapted from Dunn et al. 2011) A new drug is being extracted from an organic phase into two aqueous phases. The volumetric flow rates of the two organic-phase constituents are H and K, respectively. The volumetric flow rates of the two resulting aqueous phases are denoted by L and M Four different experiments are run by varying H, K, L, and M simultaneously, as shown in the table below, to achieve the same concentration of the drug (y, w, x, and z, respectively) in each trial. The total mass of the solute entering each experiment is given by F. Estimate the concentrations of the drug in each of the four streams. The governing equation for mass distribution of the drug between the four liquid streams for any single experiment is given as: Experiment No. M (L/min) F (Total mass H (L/min) 100 80 140 90 K (L/min L (L/min 125 110 80 04.8 125 120 120 6235 25 100 137.33 6625 5290 7300 6539 Your submission should include a MATLAB-published report that shows both your function and the results to the problem, as well as your original MATLAB code (all necessary files). Submit the completed challenge problem using the link on Canvas