My idea is that the vector space W1∩W2 is a subspace of both W1 and W2, and so it has a basis B which is a linearly independent subset of both W1 and W2. We know that we can always take a linearly independent subset of a vector space and complete it to a basis of that space, and so do that with B for W1 to obtain B∪S1, and also do that for W2 to obtain B∪S2.
Where do I go from here, and how can I use it to get the W1+W2 side?
