Answer
See below
Work Step by Step
We have $v$ is an arbitrary vector in $V$
Since $\{v_1,v_2,...,v_k\}$ is a basic for $V$, we can obtain $v=a_1v_1+a_2v_2+....a_kv_k$ with unique scalars $a_1,a_2,...,a_k$.
Thus:
$T(v)=T(a_1v_1+a_2v_2+...+a_kv_k)\\
=a_1T(v_1)+a_2T(v_2)+...+a_kT(v_k)\\
=a_10+a_20+...+a_k0\\
=0$ for all $v \in V$
Hence, $T$ is a the zero transformation.
