function [U] = GaussElim(A) %Gauss Elimination for Regular Matrix
        % This is certainly NOT the right way to do this with Matlab, which
        % has sophisticated matrix manipulation routines. This is provided
        % merely to illustrate the algorithm  in Olver
        %
        %  To use, create a matrix 
        %   > A = rand(5,10)
        % and type
        %  > [U] = GaussElim(A)
[m,n] = size(A);
U = A;
for j = 1:n                 % Choose jth column
    for i = j+1:m           % Zero elements below pivot (j,j)
        if(U(j,j) == 0)
            error('%d th Pivot vanishes. Matrix is not Regular',j)
        end
        l = U(i,j)/U(j,j);  
        for k = j:n         % Rowk -> Row k - l*Row j
            U(i,k) = U(i,k) -l*U(j,k);
        end
    %U                       % uncomment this to print result after each row reduction
    end
end