We have the following linear system of equations:
$A=\begin{pmatrix}1 & 1& 2\\ 3 & 4 & 6\\ 2 & 2 & 5\end{pmatrix}$, $\vec{b}=\begin{pmatrix}2\\ 7\\ 3\end{pmatrix}$
I want to solve the homogeneous and the inhomogeneous system, and to find a basis for the space of the solutions of the homogeneous system.
I have found that $Ax=0 \Rightarrow x=0$. Wihch is the a basis for the space of the solutions of the homogeneous system?