MATLAB: Is the own echelon function printing incorrect matrix

echelon

I am trying to create an echelon function, however, I am having trouble debugging my error. It works for almost all matrices but for the following matrix it gives an incorrect result:
A=[1 2 3 ; 1 2 4 ; 1 2 4]
echelon(A)
function x = echelon(A)
[m,n]= (size(A)); % m= rows , %n= columns
j=1;
i=1;
    while( i <m )
        for k=i+1:m
        if (A(i,j)==0)
        C = A(i,:); %Let C be the ith first row of the matrix
        A(i,:)= A(i+1,:);%Exchange the row with the one below it
        A(i+1,:) = C %Let C be the row that was above now (This code swaps rows)
       end 
        if ~all(A(k,:)==0) %check to see if row of zeros or not
        A(k,:)=A(k,:)-((A(k,j)/A(i,j))*A(i,:)) %zero out corresponding row
        end
        end
    j=j+1;
    i=i+1;
    end     
x=A
end
It gives the following incorrect result:
1 2 3
0 0 1
0 0 1
Also for the following matrix:
A=[1 2 3 ; 1 2 5]
gives the following incorrect result:
1 2 3
0 0 2

Best Answer

I haven't checked all of your code, but I assume this:
if ~all(A(k,:))==0 %check to see if row of zeros or not

was meant to be this instead:
if ~all(A(k,:)==0) %check to see if row of zeros or not
Also, you divide by A(i,j) before checking to see if it is 0.
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