Give an example (including details) of the following or briefly justify why such an example does not exist. (3.1) A 2 x 2 matrix which is not diagonalizable, but whose eigenvectors span R2. (1) (3.2) An orthogonally diagonalizable matrix that is not orthogonal. (1) (3.3) An invertible linear transformation T: P3 + R3. (1) Give an example (including details) of the following or briefly justify why such an example does not exist. (3.1) A 2 x 2 matrix which is not diagonalizable, but whose eigenvectors span R2. (1) (3.2) An orthogonally diagonalizable matrix that is not orthogonal. (1) (3.3) An invertible linear transformation T: P3 + R3. (1)