Prove that the V' obtained from the QR-factorization in Section 1.1 provides the orthogonal projection onto the orthogonal complement of e given by the formula P:=P, :=VVT, Prove that diag(P) = (1 %)e, and P;; = 1,i # j. (Hint: Consider a standard formula in textbooks for the projection onto v+ for any vector v.)