Question

Does \[\left[\begin{matrix}1 & 2 \\ 0 & 0\end{matrix}\right],\left[\begin{matrix}0&1 \\ 0 & 0\end{matrix}\right],\left[\begin{matrix}1 & 0 \\ 1 & 0\end{matrix}\right],\left[\begin{matrix}1 & 0 \\ 0 & 0\end{matrix}\right]\] span the space \[M _{2\times2}(\mathbb{R})\]