As I understand it, the two things that define a transformation as linear are:
1) $T(u+v) = T(u)+T(v)$
2) $T(cu) = cT(u)$
I want to prove that $T(x,y) = x+y+1$ (where $T: \mathbb{R}^2\to \mathbb{R}^3$ and $x,y$ are the standard coordinates in $\mathbb{R}^2$) is not a linear transformation using the rules stated above.
I was told I could show that $T(0)\ne0$ but I don't understand how that would suffice given the definition of a linear transformation.