4. Let V be finite-dimensional vector space and W a subspace. Suppose that \{b_1,..., b_n\} is a
basis for W and extend this to a basis \{b_1,..., b_k, b_{k+1},..., n\} for V using Proposition 1.4.11.
Prove that the set of vectors \{b_{k+1} + W,..., b_n + W\} is a basis for the quotient space V/W.
Proof. Write your proof here.