Example CSOCD expresses the column space of the coefficient matrix from Archetype D (call the matrix $A$ here) as the span of the first two columns of $A$. In Example CSMCS we determined that the vector \begin{equation*} \vect{c}=\colvector{2\\3\\2} \end{equation*} was not in the column space of $A$ and that the vector \begin{equation*} \vect{b}=\colvector{8\\-12\\4} \end{equation*} was in the column space of $A$. Attempt to write $\vect{c}$ and $\vect{b}$ as linear combinations of the two vectors in the span construction for the column space in Example CSOCD and record your observations.