Let me start from defining the notation of the fundamental subspaces of matrix, which can simply denote by using the Moore-Penrose generalized inverse, for help to grasp more easily the meaning of expressions presented in this paper. The following topics have been presented, for examples, (1) Relation between actual solution and solution of new variable by a change of variables is shown. (2) It’s possible for displacement and stress to express to each other as functions of common variables from both of compatibility equation and equilibrium equation. Then, as applications of the functions, derivations of rigid-body stress and displacement under conditions of zero stress and zero loading have been shown.