Are you familiar with this criteria for vector subspaces:
Let be a subset of a vector space over a field . is subspace of if and only if:
2. For all , exists .
Try to use this for your problem.
Here's an example for the first part:
First you determine that the given set is not empty, well clearly is of the form , so so .
Second, let be some arbitrary vectors and let be some complex scalars. now .