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).