I come up with following two equations $\,c,w\in \mathbb{R}\:q,b\in\mathbb R^{m}, A$ is $m\times m$ matrix, and $p$ is a $1\times m$ vector. I am trying to show that $b\in Col(A)$
$$ c+q^Tb=w\implies q^Tb=w-c\\ q^TA=p\implies q^T=pA^{-1}\\ \text{by substituttion}\quad pA^{-1}b=(w-c) $$
End up here I have no idea how to proceed further, I felt there is some technique that can put $A^{-1}$ on the right-hand side.
Sincerely thank you for your help.