$$\begin{bmatrix}a&b\\\\c&d\end{bmatrix}\mapsto \begin{bmatrix}ad-bc\\\\0\\\\0\end{bmatrix}$$
If it is linear I need to find a basis for the kernel and image but I am struggling to do this so i don't think it's linear but I have no idea why.
$$\begin{bmatrix}a&b\\\\c&d\end{bmatrix}\mapsto \begin{bmatrix}ad-bc\\\\0\\\\0\end{bmatrix}$$
If it is linear I need to find a basis for the kernel and image but I am struggling to do this so i don't think it's linear but I have no idea why.