Let $B=\begin{Bmatrix}v_1, v_2, v_3, v_4\end{Bmatrix}$ base of a vector space $V$
And $S=\left \langle v_1 + 2v_2, v_2 + v_3 \right \rangle$ and $T=\left \langle v_3 + v_4, v_1 + v_2 + v_4 \right \rangle$
Find a vector $v \in S + T$ so that $v \notin S$ and $v \notin T$
I know $S + T = \langle v_1 + 2v_2, v_2 + v_3, v_3 + v_4, v_1 + v_2 + v_4 \rangle$, but I can't figure out how to find the vector the problem asks.
Thanks in advance for your time.