1. Consider the 4 by 3 matrix o -N A = (i) (3 marks) Compute the matrix B = A A and the eigenvalues of B. (ii) (2 marks) For each eigenvalue in (i), find a unit eigenvector. (iii) (2 marks) Find an orthogonal diagonalization of decomposition B, i.e. find an orthogonal matrix E and a diagonal matrix D such that B = EDE . (iv) (5 marks) Find a singular value decomposition (SVD) of the matrix A, i.e. find an orthogonal matrix U, a diagonal matrix E and an orthogonal matrix V such that A = UEVT