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:

1. .

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 .