I am looking to demonstrate that the X solutions matrix to a linear compatible system of equations (A|b) and B being a generalized inverse of A; such that ABA=A, can be expressed as:
X = B · b + (B · A -$I_m$) · $\begin{bmatrix}k_1 \\ ... \\ k_2\end{bmatrix}$
being $k_1, ..., k_2$ K values.
I am thinking of using PAQ-reduction to prove this. However, I haven't got quite clear the ideas on how to start, or whether which demonstration.