How do I find the coordinate vectors of this matrix set? $$\left[ \begin{matrix} 1&2& \\ -1&0\end{matrix}\right]$$ $$\left[ \begin{matrix} 0&-1& \\ 1&1\end{matrix}\right]$$ $$\left[ \begin{matrix} 1&0& \\ 1&2\end{matrix}\right]$$
in $$M_2,_2$$
I have a feeling that the coordinate vectors are just $\{(1,2,-1,0), (0,-1,1,1),(1,0,1,2)\}$.
Do correct me if I'm wrong
There is no unique answer to your question. The vector space $$M_{2x2}$$ is isomorphic to $$R^{4}$$, so if you pick the standard base, your answer is correct. If you picked another base, the answer would’ve been different.