Gaussian Elimination script question

Hi, I want to solve Ax = b. A is mxn and b is nx1. Thus x is nx1.

I want to print two answers (which satisfies Ax = 0 and Ax = b)

but i couldn't proceed further than this one. in line 8, if i have 0 in A(k,k), i need to swap k th row with another row (bigger than k) or make pivot in other column but I couldn't do it.

for example, if A is [1,3,3,2;2,6,9,5;-1,-3,3,0] and b is [1;5;5],

[1,3,3,2;2,6,9,5;-1,-3,3,0] becomes [1,3,3,2;0,0,3,1;0,0,0,0] after one procedure. I need help please : )

function x = gaussianelim(A,b)
 [row,col]=size(A);
m = row;
n = col;
x = zeros(m,1);
   for k=1:m-1   
    for i=k+1:m
        mul = A(i,k)/A(k,k);
        for j=k+1:n
            A(i,j) = A(i,j)-mul*A(k,j);
        end
        b(i) = b(i)-mul*b(k);
    end
  
   end
 

Answer 1

[Dinesh Yadav]

Kindly go through the following links.

https://www.mathworks.com/matlabcentral/answers/43397-performing-gauss-elimination-with-matlab

https://www.mathworks.com/matlabcentral/fileexchange/13451-gauss-elimination-with-complete-pivoting

Hope it helps.