Let 6 3 -6 A = 4 (a) (3 marks) Find the characteristic polynomial and the eigenvalues of A. Hint: To help you factor out the characteristic polynomial, start with det(A - 1I) and apply a column operation to put a zero in entry (3,1) and then a row operation to put a zero in entry (2,1) : then expand the determinant along the first column. This way, you will be able to obtain at least one factor of the characteristic polynomial. (b) (3 marks) Find a basis for each eigenspace of A. (c) (2 marks) If A is diagonalizable, then diagonalize A, that is, find an invertible matrix P and a diagonal matrix D such that P- AP = D. If A is not diagonalizable, then explain why it is not diagonalizable