Math 6410 • ODE

\begin{enumerate}
\item[(a)] What does Floquet's Theorem say about solutions of linear \(n\times n\)
systems \(X'=A(t)X\) (\(A\) is a continuous \(n\times n\) matrix)?

\item[(b)] Show that, given any \(n\times n\) matrices \(B\) (constant) and \(A(t)\)
(continuous), there is a change of variables \(Y=P(t)X\) which reduces the system
\(X'=A(t)X\) to the system \(Y'=BY\).

\item[(c)] Show that there is a particular choice of \(P(t)\) and \(B\) that is related
to Floquet's Theorem. Why might you be interested in that choice?
\end{enumerate}