 expect to have when we are done multiplying matrices?</li>

      <li>What are $\partial \vec F/\partial p$ and $\partial \vec
      F/\partial q$?</li>
    </ol>
  </div>

  <div class="problem-nonum" label="Challenge">(Optional challenge)
    Suppose $\vec F(u,v) = (3u-v,u+2v,3v)$, $\vec G(x,y,z)=(x^2+z,
    4y-x)$, and $\vec r(t) = (t^3, 2t+1, 1-t)$. We want to examine
    $\vec F(\vec G(\vec r(t))$. This means that $\vec F\circ \vec
    G\circ \vec r$ is a function from $\RR^n\to\RR^m$ for what $n$
   