Find all eigenvalues corresponding to each given matrix and their corresponding algebraic multiplicities. Also, express each eigenspace as a set of linear combinations of fundamental eigenvectors.
(a) $\left[\begin{array}{ll}1 & 3 \\ 0 & 1\end{array}\right]$
(b) $\left[\begin{array}{rr}2 & -1 \\ 0 & 3\end{array}\right]$
(c) $\left[\begin{array}{rrr}1 & 0 & 1 \\ 0 & 2 & -3 \\ 0 & 0 & -5\end{array}\right]$
(d) $\left[\begin{array}{cc}8 & -21 \\ 3 & -8\end{array}\right]$
(e) $\left[\begin{array}{lll}4 & 0 & -2 \\ 6 & 2 & -6 \\ 4 & 0 & -2\end{array}\right]$
(f) $\left[\begin{array}{rrr}3 & 4 & 12 \\ 4 & -12 & 3 \\ 12 & 3 & -4\end{array}\right]$
(g) $\left[\begin{array}{rrrr}2 & 1 & -2 & -4 \\ -2 & -4 & 4 & 10 \\ 3 & 4 & -5 & -12 \\ -2 & -3 & 4 & 9\end{array}\right]$
(h) $\left[\begin{array}{rrrr}3 & -1 & 4 & -1 \\ 0 & 3 & -3 & 3 \\ -6 & 2 & -8 & 2 \\ -6 & -4 & -2 & -4\end{array}\right]$