Problem 3: GE with partial pivoting (MATLAB) 1. Develop, debug and test a program in MATLAB to solve a system of equations using Gauss elimination with partial pivoting. Base the program on pseudocode included below in Figure 1. Let the first line of the function be: function x = GaussPivot (A,b). 2. Test the program using the following system of equations, 4x1+x2-3 = -2, 5x1 + x2 + 2x3 = 4, 6x₁ + x₂ + x3 = 6. (5) 3. Modify the function so that it computes and returns the determinant (with the correct sign), and detects whether the system is singular based on a near-zero determinant. Define "near-zero" as being when the absolute value of the determinant is below a tolerance. When this occurs, design the function so that an error message is displayed and the function terminates. Let the first line of the new function be: function [x, D] = GaussPivotNew (A, b, tol).