Once again all one must is to check two conditions:
1) is the set closed with respect to addition?
2) is the set closed with respect to scalar multiplication?
all A where is the definition of your first subset. From there you need to prove that the summation of two elements from the subset results in an element of your subset and that any scalar multiplication also has the same result (definition of a subspace).
e.g. Can you prove that and where ?