Geometic non linear problem for deep truss element

Hi,

Anyone, has read these lecture notes:

http://www.colorado.edu/engineering/cas/courses.d/NFEM.d/NFEM.Ch08.d/NFEM.Ch08.pdf

I've programmed FEM analysis for a deep truss element-but find my assembled stiffness matrix after application of boundary conditions singular--

My question is, whether can we apply above stiffness matrix (as in the chapter) for a truss as shown in the attached figure (jpg file)?

plz help