Prove or disprove that base of space is base of subspace Let vectors $v_1,v_2,v_3,v_4$ is base of space $V$, and if $W$ is subspace of $V$ such that $v_1,v_2\in W$ and $v_3,v_4\not \in W$ then $v_1,v_2$ is base of $W$?
My Professor said that you can not make a base of subspace from base of space, but you can make a base of space from base of subspace.
But here I do not know how to prove, can you help me? 

Since $v_1,v_2,v_3,v_4$ is base of space $V$, $W$ is subspace of $V$ and $v_1,v_2\in W$ 
we know that $\dim W\ge 2.$
But it is possible to have $\dim W=3.$ For example, assume $v_3+v_4\in W.$ That is, consider $W=span\{v_1,v_2,v_3+v_4\}$
