We introduce the Column Space of $\mathbf{A}$, the place where $\vec{b}$ must live if $\mathbf{A}\vec{x}=\vec{b}$ has a solution (one or infinitely many). Column Space is the first of four fundamental subspaces that will help us deeply understand our friend $\mathbf{A}\vec{x}=\vec{b}$. Finding Column Space will come soon.