
<ol>
<li>The matrix below is nonsingular.  What can you now say about its columns?
\begin{equation*}
A= \begin{bmatrix}
-3 &amp; 0 &amp; 1\\
1 &amp; 2 &amp; 1\\
5 &amp; 1 &amp; 6
\end{bmatrix}
\end{equation*}
</li>
<li>Write the vector $\vect{w}=\colvector{6\\6\\15}$ as a linear combination of the columns of the matrix $A$ above.  How many ways are there to answer this question?
</li>
<li>Why is an orthonormal basis desirable?
</li>
</ol>