{6 marks.) Let 0: A: 1-th MON GOMrP- You are given that the characteristic equation of A is (A +1)2(A 8) = U, i.e. the eigenvalues of A are A = 1.. 8. (3} Find the eigenvectors of A. (b) Are the eigenvectors of A corresponding to the eigenvalue A = 1 orthogonal with respect to the usual dot product? If not, appl}.r the GramSchmidt process to turn them into an orthonormal set of eigenvectors. (c) Find an orthogonal matrix P that orthogonally diagonalizes A. {3 marks.) Let at, y, z} = $2 + y2 + :52 + 46 y; be a quadratic form, where b E R. Suppose that after the variable change, 113' 1!}. y =P v .. Z 11! where P is an orthogonal matrix, the quadratic form becomes f = 11-2 + 21)? in terms of the new variables 11,1) and in. Determine all possible values for b