Determining Whether a function is linear I'm positive this function is linear but am having trouble showing it:
Determine whether $T:V \to W$ defines a linear transformation:
$V=R^3$, $W=R$ 
$T((a_1, a_2, a_3)) = 3a_1 +2a_2 + a_3 $
I know I have to show that $T(u+v) = T(u) + T(v)$ and $T(cu) = cT(u)$ but am unsure how to proceed.

These are the steps you should take to prove $T(u+v)=T(u)+T(v)$.


*

*Set $u=(u_1,u_2,u_3)$ and $v=(v_1,v_2,v_3)$.

*Write down what $T(u)$ is.

*Write down what $T(v)$ is.

*Write down what $T(u)+T(v)$ is.

*Write down what $u+v$ is.

*Write down what $T(u+v)$ is.

*Compare results from (3) and (5).


Which of these steps were you able to do, and where are you stuck?
