Define $T: \mathbb{R}^3 \rightarrow \mathbb{R}^2$ by $T(x,y,z) = (2y + z, x-z)$. Find $\mbox{ker}(T)$ and $\mbox{range}(T)$
I could find the kernel easy enough, and ended up getting $\{(-2x, x, -2x) : x \in \mathbb{R}\}$ but I don't really know how the get the range. In this case isn't the range effectively just the set with elements satisfying the equation $T$? I'm not really sure what the question is wanting to be honest. Some help would be great.
Thanks