Q}: T/F? An n x n matrix is invertible if and only if it does not have 0 as an eigenvalue. Q2: T/F? A 3 x 3 matrix may have 4 distinct eigenvalues. Q3: T/ F? If v and w are two linearly independent eigenvectors of an n x n matrix, then the eigenvalues corresponding to v and w are distinct. Q4: T/ F? Every n x n matrix must have at least one real eigenvalue. 05: T/ F? There cannot be more than n eigenvalues of an n x n matrix. Q6: T/F? It a is an eigenvalue of an n x n matrix A. then a'2 is an eigenvalue of NZ. Q7: T/ F? ii A is an n x n matrix such that A'100 = 0, then the only eigenvalue A can have is 0. :n. -:i- 'r '. L'A':'_ . ' 08 (Hard): T/F? Let A be an n x n matrix, and suppose that A has n real eigenvalues counting with multiplicities. Then the sum of all the eigenvalues (counting with multiplicities) is equal to the sum of all the diagonal entries of A. {3 _-'._;v-r'-:Ct'-:'.,;":_; . 09: Let A be an n x n matrix. is it possible to have a row'operation on A that changes all the eigenvalues of A? if so, give a specific example. '