6. NO Let A = 1 P 1 0 , and D = NOO We have A = PDP . Which of the following statements is true? 0 O (1 mark) O The eigenspace E2 associated to the eigenvalue 2 has dimension 1. O is an eigenvector of A associated with the eigenvalue 1. OHH is an eigenvector of A associated with the eigenvalue 2.7. Suppose A is a symmetric matrix or order n. Which of the following statements are true? (1 mark) We can always find a basis of R" consisting of eigenvectors of A. A is diagonalizable. Let A be an eigenvalue of A. Then any basis S = {ul, ..., uk} for the eigenspace Ex must be orthogonal. O For every distinct eigenvalues 1, 12 of A, the eigenspace Ex, associated to 1 is orthogonal to the eigenspace Ex, associated to 12.8. Let A be a diagonalizable matrix. By applying the Gram-Schmidt process to the bases of the various eigenspaces of A, we can always orthogonally diagonalize A. (1 mark) O True O False