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\begin{document}
\begin{center}
{\bf Homework 8}\\
(due Wednesday, November 2)
\end{center}
\vspace*{.3in}

\noindent{\bf Book Problems:} 
\begin{description}
\item[3.4, page 89] 4.3
\item[3.5, pages 94-95] 5.2, 5.3, 5.4 (last two only), 5.5, 5.6
\end{description}

\begin{prob}
Suppose you want to find the $1001$st Fibonacci number following the ideas I
gave in class (i.e. by finding the $1000$th power of a $2 \times 2$ matrix). Even without using ideas
connected with eigenvalues and eigenvectors, you can compute this power by doing far fewer
than 1000 matrix multiplications. How can this be done, and precisely how many matrix
multiplications will it take? (Hint: you can compute $A^8$ by doing only 3 multiplications.
How?).
\end{prob}



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