MATLAB: I need help in developing a function file GE_m(A,b) to determine the pivot row r such that a(rk) is the first nonzero entry among a(kk),a(k+1)…a(n,k). if a(kk)=a(k+1,k)=a(nk)=0 then pivot out that ‘A is not invertible’ and quit.

Question

%I need help in developing a function file GE_m(A,b) to determine the pivot row r 
% such that a(rk) is the first nonzero entry among a(kk),a(k+1)...a(n,k). 
% if a(kk)=a(k+1,k)=a(nk)=0 then pivot out that 'A is not invertible' and quit. 
% this is the other function i will be calling in my comand window and this function is correct
%function x=ut_sys(U,c)
%n=length(U);
%x=zeros(n,1);
%x(n)=c(n)/U(n,n);
%for i=n-1:-1:1
%    s=0;
%    for j=n:-1:i+1
        %s =s+U(i,j)*x(j);
%    end
       
%        x(i) = (c(i)-s) /U(i,i);
%end

%end
% i need help with the function below!! i cannot get it working
function [A,b]=GE_m(A,b)
n =length(b);
for k=1:n-1
    ap=abs(A(k,k));
    r=k;
    
    while ap < (n)*e-15
        r=r+1;
    end
end
        if ap , (n)*e-15
            disp('A is not invertible');
        end
    
end

Answer 1

The following problem can be solved by using nested for loop. Refer to the following code to see how to solve this:

function [A,b]=a1(A,b) 
n =length(b); 
flag = 0; 
for k=1:n-1 
    for i = k:n-1 
        if(a(k,i) ~= 0) 
            flag = 1; 
        end 
    end     
end 
if(flag == 1) 
    disp('A is not invertible') 
end 
end