function x = lauchli_null_left ( alpha, m, n )

%*****************************************************************************80
%
%% LAUCHLI_NULL_LEFT returns a left null vector of the LAUCHLI matrix.
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    08 March 2015
%
%  Author:
%
%    John Burkardt
%
%  Input:
%
%    real ALPHA, the scalar defining the matrix.
%
%    integer M, N, the order of A.
%    It should be the case that M = N + 1.
%
%  Output:
%
%    real X(M,1), the vector.
%
  x = zeros ( m, 1 );

  x(1,1) = - alpha;
  x(2:m,1) = 1.0;

  return
end
