I want to preface this by saying I don't have the answer. I haven't taken linear algebra yet. If someone here does know the answer, by all means, their answer should supersede mine. But... if
[tex] A= \left[\begin{array}{ccc}-2&-1&0\\0&1&3\\1&1&6\\2&1&-12\end{array}\right][/tex]
then here is an outline of how to determine whether the columns form a linearly independent set.
