Question

$$f(\begin{matrix}x\\ y\\ z\end{matrix})=(\begin{matrix}2x+y\\ y-x\\ 2y+4z\end{matrix})$$

Solve for x, y, z

$\left\{\begin{matrix}x=0\text{, }y=0\text{, }z=0\text{, }&f\neq 4\\x=0\text{, }y=0\text{, }z\in \mathrm{R}\text{, }&f=4\end{matrix}\right.$