Let A be the reduced incidence matrix for a structure and C the diagonal bar stiffness matrix.

Question:

Let A be the reduced incidence matrix for a structure and C the diagonal bar stiffness matrix. Suppose f is a set of external forces that maintains equilibrium of the structure.
(a) Prove that f = ATCg for some g.
(b) Prove that an allowable displacement u is a least squares solution to the system A u = g with respect to the weighted norm ||v||2 = vTC v.