How would I go about finding out if these functions are linear because it is in $\mathbb R^3$ and also in $\mathbb R^2 $.

$ T: \mathbb R^3\to\mathbb R $ with $T(x,y,z)=(x+y+z+1).$
and this question too. $T: \mathbb R^3 \to \mathbb R^3$ with $T(x,y,z)=(2x-y+z,x-2zy)$