Answer
No.
Work Step by Step
We know that if $av_1+bv_2=v$, then $3a-2b=1,a-b=1,2a+b=-2$.
Thus $(a-b)+(2a+b)=1-2\\3a=-1\\a=-1/3$
$a-b=-1/3-b=1\\b=-4/3$
And this doesn't satisfy the last equation because$3(-1/3)-2(-4/3)=-1+8/3=5/3\ne1$, thus it is not in the span.
