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\homework{3: Discrete Dynamical Systems and the Internet}{Due Tuesday, Week 4, at the start of class}
Work on these problems for 90m/until you solve everything/longer if you're interested!
\begin{enumerate}
\item Consider the following ``miniature'' model for the internet, made of six webpages\footnote{These were all real websites, once upon a time.  Even DigiScents.  People once thought smelling things over the internet was a good idea.}:
\begin{multicols}{2}
\begin{itemize}
\item Pets.com: links to boo, Webvan, and Kozmo.
\item boo.com: links to Webvan, Kozmo and eToys.
\item Webvan.com: links to Kozmo, eToys, and DigiScents.
\item Kozmo.com: links to eToys, DigiScents, and Pets.com.
\item eToys.com: links to DigiScents, Pets, and boo.
\item DigiScents.com: links to Pets, boo, and Webvan.
\end{itemize}
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\begin{enumerate}
\item Draw a diagram with six bubbles, one for each webpage, and arrows between these bubbles representing the links above.
\item Turn this model of the internet into a $6 \times 6$ ``link-matrix'' $A$, as done in the notes.
\item Use this link matrix to find the ``importance vector'' (i.e. eigenvector corresponding to the eigenvalue 1) for this matrix $A$, showing your work and justifying your answer.  Interpret your results: what do they say about the relative importance of these six websites?
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\end{enumerate}
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