An n x n matrix A is diagonalizable if and only if A has n linearly independent eigenvectors. Find the characteristic polynomial, eigenvalues, and eigenvectors of each of the following matrices, if they exist. [1 2 3 -2 0 0 (1) (2) 0 2 3 "[ 2 3 3 4 -1 6 0 0 3 0 1 0 1 1 0 1 0 (5) (6) 0 1 0 1 1 [10 002 Hint: (1) is diagonal. (2) is triangular. (4) and (5) are symmetric. (6) has two nonzero blocks, each of which is skew-symmetric. 11 TE " (3) 0-5 0 00 0800 13 CONO 0 00-2