A basis has three properties:

a) the vectors are independent

b) the vectors span the space

c) the number of vectors in the set is equal to the dimension of the space.

Further, any two of those is sufficient to prove the third.

Ifyou know the dimension of the subspace and can see that the number of vectors in the given set is equal to that, then you only need show that they are independentorthat they span the space.