Hey Tra003.

For a basis, you need N linearly independent vectors where dim(V) = N. Once you have this, you definitely have a basis for any vector space.

For the second one you should show that the two spaces are independent. If you are talking about two vectors then showing they are independent (i.e. not scalar multiples) of each other should suffice and you can do this by setting up a two row matrix and row-reducing it.