Span(S) and Subspaces

Question

How can you tell what plane specifically a vector set spans? For example S: (1,0,0), (0,1,1). What plane does this vector set span specifically and how can you see that?

Thanks

Answer 1

Let $V$ be a vectorspace over the field $F$. If $S=\{v_1,v_2,v_3,...,v_k\}\subset V$. Then, $Span S=\{a_1v_1+a_2v_2+...+a_kv_k|a_1,a_2,...,a_k \in F\}.$