In the last 2 lectures of linear algebra we have talked about linear mappings and other stuff, but I missed actually the last one and I am quite in bad situation.
What matrix transforms $\left(\begin{matrix} 1 \\ 0\end{matrix}\right)$ into $\left(\begin{matrix} 2 \\ 6\end{matrix}\right)$ and tranforms $\left(\begin{matrix} 0 \\ 1\end{matrix}\right)$ into $\left(\begin{matrix} 4 \\ 8\end{matrix}\right)$?
I think I understood what I need to find: a matrix that multiplies our initial matrix formed by our initial vectors $$\left(\begin{matrix} 1 & 0 \\ 0 & 1\end{matrix}\right)$$
and the resulting matrix is:$$\left(\begin{matrix} 2 & 6 \\ 4 & 8\end{matrix}\right)$$
Am I right?
Is there a way to automate this process?
