function N = nulbasis_modified(A)

% modified by 
% -----------
% name:   Ahmed Turk
% class:  Linear Algebra and Applications 
% prof. \ Roe Goodman
% reason for modification:
%  the previous version returns error when the matrix has only
%  the empty vector as the null basis (when the rank(r)= no. of columns)
%
% N = nulbasis_modified(A) returns a basis for the nullspace of A
% in the columns of N. The basis contains the n-r special 
% solutions to Ax=0.  freecol is the list of free columns.
%
% Example:
%
% >> A = [1 2 0 3;
%        [0 0 1 4];
%
% >> N = nulbasis_modified(A)
%
%    N = [-2  -3]   
%        [ 1   0]
%        [ 0  -4]
%        [ 0   1]
%
% See also fourbase.

[R, pivcol] = rref(A, sqrt(eps));
[m, n] = size(A);
r = length(pivcol);
if r == n 
   N='empty basis--zero subspace';
else
   freecol = 1:n;
   freecol(pivcol) = [];
   N = zeros(n, n-r);
   N(freecol, : ) = eye(n-r);
   N(pivcol,  : ) = -R(1:r, freecol);
end;