6. Suppose S = {u1, u2, us} is a linear independent set in R". Let v1 = 2u1 + u2-3u3, V2 = U1 - U2, V3 = U2 + Us. (a) Let 01, 02, 03 be real numbers, expand 01V1 + 02V2 + 03V3 = Blu1 + Bu2 + Bus. Find 81, 82, 83 in terms of 01, 02, 03. (b) Suppose 01V1+ 02V2+ 03V3 = 0, show that 81 = 32 = 83 = 0. (c) Is { v1, v2, v3} linearly independent? (d) If S = {ul, u2, u3} is not linear independent and u; / 0 for i = 1, 2,3, is {V1; V2, V3} linearly independent? If yes, prove it. If not, find an example