5. Let Vi and V2 be subspaces of R" defined by V1 = {(x1 , ..., Xn) |xi+ ...+ Xn =0) and V2 = {(x1,. .., Xn) | x1 = . .. = Xn). Prove that any vector v E R" can be uniquely expressed as v = v1 + 02 such that vl E Vi and U2 E V2 .6. Let S = {'01, . . . ,vn} be a basis for R", and let P = (2:1 '0") (each U] is a column vector). Prove that for any square matrix A of order n and column vector 'v E R", [5] [A1213 = P'lAPlv13. [Hint Express 17 has a linear combination of '01, . . . , 17\".]