Linear programming: basic solution?
If the matrix consists of $$\begin{bmatrix}1&-2&0&0&0\\-3&6&1&3&0\\0&0&2&6&-1\end{bmatrix},$$ how is it that there are 4 basic solutions? It says that the first and second columns, as well as the third and fourth columns are scalar multiples, but what does that have to do with basic solutions?