Can a vector space have multiple spanning sets? Maybe this is obvious, but can a vector space have multiple spanning sets or is there only a single spanning set for every vector space?
Thanks

Of course there are multiple sets.
Even for just one-dimensional vector spaces, at least over fields with more than two elements, every non-zero scalar is a spanning set.
If $\{v_1,\ldots,v_k\}$ spans $V$ then $\{v_1+v_2,v_2,\ldots,v_k\}$ is a different spanning set, and one can replace more vectors by others, or by more complicated expressions.
In fact if $V$ is spanned by $v_1,\ldots, v_k$ and $v\in V$ is a vector such that $v=\sum_{i=1}^k\alpha_i v_i$, and $\alpha_i\neq 0$ then we can show that $\{v_1,\ldots,v_{i-1},v,v_{i+1},\ldots,v_k\}$ is a spanning set.
Furthermore! If we only require spanning the space, and not being linearly independent then there are even more spanning sets than that. Anything which contains a basis, really.
