Find the eigenvalues and eigenvectors of the following matrices:
(a) $\left(\begin{array}{rr}1 & -2 \\ -2 & 1\end{array}\right)$,
(b) $\left(\begin{array}{ll}1 & -\frac{2}{3} \\ \frac{1}{2} & -\frac{1}{6}\end{array}\right)$,
(c) $\left(\begin{array}{rr}3 & 1 \\ -1 & 1\end{array}\right)$,
(d) $\left(\begin{array}{rr}1 & 2 \\ -1 & 1\end{array}\right)$
(e) $\left(\begin{array}{rrr}3 & -1 & 0 \\ -1 & 2 & -1 \\ 0 & -1 & 3\end{array}\right)$,
(f) $\left(\begin{array}{rrr}-1 & -1 & 4 \\ 1 & 3 & -2 \\ 1 & 1 & -1\end{array}\right)$,
(g) $\left(\begin{array}{rrr}1 & -3 & 11 \\ 2 & -6 & 16 \\ 1 & -3 & 7\end{array}\right)$,
(h) $\left(\begin{array}{rrr}2 & -1 & -1 \\ -2 & 1 & 1 \\ 1 & 0 & 1\end{array}\right)$,
(i) $\left(\begin{array}{rrr}-4 & -4 & 2 \\ 3 & 4 & -1 \\ -3 & -2 & 3\end{array}\right)$,
(j) $\left(\begin{array}{llll}3 & 4 & 0 & 0 \\ 4 & 3 & 0 & 0 \\ 0 & 0 & 1 & 3 \\ 0 & 0 & 4 & 5\end{array}\right)$,
(k) $\left(\begin{array}{rrrr}4 & 0 & 0 & 0 \\ 1 & 3 & 0 & 0 \\ -1 & 1 & 2 & 0 \\ 1 & -1 & 1 & 1\end{array}\right)$.