Why is my own echelon function printing incorrect matrix

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

[James Tursa]

Are you trying to produce any row echelon form, or the reduced row echelon form?

[Natalie Murawski]

Just echelon form, not reduced echelon form, so just with 1 as pivots.

Answer 1

[James Tursa]

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.

[Natalie Murawski]

Thanks, I fixed that, but I moved the checking if A(i,j) is 0 above gives this result:

1 2 3

0 0 1

NaN NaN NaN

I must be dividing by 0 somewhere.

[James Tursa]

Best way to debug at this point is to step through your code line by line and see what is happening to A at each step. Then you can easily find where that divide by 0 is happening and correct it. If you still have problems, post your current code and ask more questions.

What algorithm are you using to ensure you are not dividing by 0? Looks like you may need to rethink how you are doing your row swapping.

[Natalie Murawski]

Alright, thank you!