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\begin{center}
  {\large Mathematics 111}\\Spring 2007\\Homework 6
\end{center}

\begin{enumerate}

\item Find all rational and Jordan canonical forms of a matrix in
  $M_5(\C)$ having minimal polynomial $x^2(x-1)$.  Be sure to give the
  corresponding invariants and the characteristic polynomial.



\item Show that any linear operator $T$ on a finite dimensional vector
  space (over a field of characteristic not equal to 2) which
  satisfies $T^2 = I$ is diagonalizable.  Give all possible Jordan
  forms for $4\times 4$ matrices.



\end{enumerate}






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