Let L be a linear transformation defined by its standard matrix AL $\begin{bmatrix}1&-1&1&2\\2&-2&3&4\end{bmatrix}$
As I understand domain and codomain of L are $L:\mathbb{R}^4 \rightarrow \mathbb{R}^2$ ?
How can I write formula definition of transformation L? I know it should look like $L(x,y,z,t) = (\ldots, \ldots,)$.
I'm not sure how to approach this problem. Could anyone explain how to solve this problem? Thanks.

See that :
$$\begin{bmatrix}1&-1&1&2\\2&-2&3&4\end{bmatrix}\begin{bmatrix}x\\y\\z\\t\end{bmatrix}=\begin{bmatrix}x-y+z+2t\\2x-2y+3z+4t\end{bmatrix}$$
$f:\mathbb{R}^4\rightarrow \mathbb{R^2}$ is given by $f(x,y,z,t)=(x-y+z+2t,2x-2y+3z+4t)$
