Suppose vectors b₁,...,b_p span a subspace W, and let {a₁,...,a_q} be any set in W containing more than p vectors. Fill in the details of the following argument to show that {a,...,aq} must be linearly dependent. First, let B = [b₁ ... b_p] and A = [a₁ ... a_q]. 

a. Explain why for each vector a_j, there exists a vector c_j in R^P such that a_j = Bc_j. 

b. Let C = [c₁ ... c_q]. Explain why there is a nonzero vector u such that Cu = 0. 

c. Use B and C to show that Au = 0. This shows that the columns of A are linearly dependent.