Find the characteristic equation and the eigenvalues (and a basis for each of the corresponding eigenspaces) of the matrix.
\[
\left[\begin{array}{rrr}
0 & -3 & 5 \\
-4 & 4 & -10 \\
0 & 0 & 4
\end{array}\right]
\]
(a) the characteristic equation
(b) the eigenvalues (Enter your answers from smallest to largest.)
\[
\left(\lambda_{1}, \lambda_{2}, \lambda_{3}\right)=(\square)
\]
a basis for each of the corresponding eigenspaces
\[
\mathbf{x}_{1}=
\]
\[
\mathbf{x}_{2}=\square
\]
\[
\mathbf{x}_{3}=
\]
\( \square \)
