Orthogonality of Left Singular Vectors (10 points) In the SVD lecture, we showed that left singular vectors are orthogonal, i.e., ui uj for i j. Here, we would like you to give another proof that is simpler assuming that you already know: (1) the right singular vectors vi of A are the eigenvectors of AT A with eigenvalues i 2 ; (2) ui = Avi /i; (3) vi vj for i j. Hint: Show that ui T uj = (j/i) vi T vj, starting from the left-hand side using (2)