Let T: $\mathbb{R}^3\rightarrow \mathbb{R}$ be linear. Show that there exist scalars a, b, and c such that $T(x,y,z)= ax + by + cz$ for all $(x,y,z) \in \mathbb{R}^3$
Can I just say "you can pick $a=b=c=0$" or do I have to actually expand out $T(kx+ x', ky + y', kz + z')$ and verify that T is linear where $k\in \mathbb{R}$?