Let MS be the n ( n matrix whose jth column is v and let MT be the n ( n matrix whose jth column is Wj. Prove that MS and MT are nonsingular. Consider the homogeneous systems MSx = 0 and MTx = 0.)
Let S = [v1, v2, ( ( ( ( vn} and T = {w1, w2, ( ( ( ( wn} be ordered bases for the vector space Rn.