Jordan canonical form of a matrix

Consider the following matrix:

A = [\begin{matrix} 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 4 \\ 0 & 0 & 0 & 0 \end{matrix}] .

Determine the characteristic and minimal polynomials of $A$ .
Find a basis for $R^{4}$ consisting of generalized eigenvectors of $A$ .
Find an invertible matrix $S$ such that $S^{- 1} A S$ is in Jordan canonical form.
Determine a Jordan canonical form of $A$ .

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Consider the following matrix:
	\[
		A=\begin{bmatrix} 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 4 \\ 0 & 0 & 0 & 0\end{bmatrix}.
	\]
\begin{enumerate}[label=\alph*)]
	\item Determine the characteristic and minimal polynomials of $A$.
	\item Find a basis for ${\bf R}^4$ consisting of generalized eigenvectors of $A$.
	\item Find an invertible matrix $S$ such that $S^{-1}AS$ is in Jordan canonical form.
	\item Determine a Jordan canonical form of $A$.
	\end{enumerate}