rref of an augmented matrix without using rref command in matlab

main.m
function [R] = rref_augmented(A,b)
% Computes the reduced row echelon form of an augmented matrix [A,b]
% without using the rref command in Matlab

[m,n] = size(A);
p = 1; % pivoting index

% loop over columns of the matrix
for j = 1:n  
    % find row with largest absolute value in j-th column
    [~,i] = max(abs(A(p:m,j))); 
    i = i + p-1; % adjust for the offset
    % swap rows p and i
    tmp = A(p,:);
    A(p,:) = A(i,:);
    A(i,:) = tmp;
    tmp = b(p,:);
    b(p,:) = b(i,:);
    b(i,:) = tmp;
    % divide p-th row by pivot
    pivot = A(p,j);
    A(p,:) = A(p,:) / pivot;
    b(p,:) = b(p,:) / pivot;
    % zero out entries below pivot
    for i = p+1:m
        factor = A(i,j) / A(p,j);
        A(i,:) = A(i,:) - factor * A(p,:);
        b(i,:) = b(i,:) - factor * b(p,:);
    end
    % move to next pivot
    p = p + 1;
    % exit loop if we have processed all rows or columns
    if p > m || p > n
        break
    end
end

R = [A,b]; % combine A and b back into one matrix
end
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main.m
A = [1 2 3; 4 5 6; 7 8 9];
b = [1; 2; 3];
R = rref_augmented(A,b)
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main.m
R =
    1.0000         0         0   -1.0000
         0    1.0000         0    2.0000
         0         0    1.0000   -1.0000
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