Answer
See below
Work Step by Step
Given: $v_1=(1,1,-1)\\
v_2=(2,1,3)\\
v_3=(-2,-2,2)$
Let $a,b$ be scalars
Obtain: $av_1+bv_2\\=av_1+bv_2+0\\=av_1+bv_2+0v_3\\
\rightarrow v \in span \{v_1,v_2\} \in S\\
\rightarrow span \{v_1,v_2\} \subset S$
We can notice that $-2v_1=-2(1,1,-1)=(-2,-2,2)=v_3$
then $av_1+bv_2+c(-2v_1)\\
=av_1+bv_2-2cv_1\\
=(a-2c)v_1+bv_2\\
\rightarrow v \in span \{v_1,v_2\}\\
\rightarrow S\in span \{v_1\}$
Geometrically span $\{v_1,v_2\}=S$ and $S$ is spanned by $v_1$ and $v_2$
