It is well known that a singular matrice appears due to the degenerate scale once the BEM is used for solving the Dirichelet problem.For solving the Neumann problem,both FEM and BEM yields a rank-deficient matrix.Fredholm alternative theorem plays an important role for the singular matrix in the linear algebra.Based on the singular value decomposition(SVD)for the singular matrix,range deficiency can be easily and systematically examined.By introducing a slack variable,we obtain a bordered matrix by adding one column vector from the left singular vector and one row vector from the right singular vector with respect to the zero singular value.It is interesting to find that an original singular matrix is regularized to a non-singular one.