{vmatrix} -b\det\begin{vmatrix}d&amp;f\\g&amp;i\end{vmatrix} +c\det\begin{vmatrix}d&amp;e\\g&amp;h\end{vmatrix}\\
&amp;=a(ei-hf)-b(di-gf)+c(dh-ge).
\end{align*}

    </div>

  <div class="problem">
    <div class="marginpar">
      For extra practice, create your own square matrix (2 by 2 or
      3 by 3) and compute the determinant by hand. Then use Sage or Wolfram
      Alpha to check your work. Do this until you feel comfortable
      taking determinants.
    </div>

    Compute $\begin{vmatrix}
1&2\\
3&