The Row Space of $\mathbf{A}$, like Column Space, is a place we need to know about too. All solutions to $\mathbf{A}\vec{x} = \vec{b}$ where $\vec{b} \ne \vec{0}$ have to come from somewhere that is not Nullspace. We show that subspace formed by all linear combinations of the rows of $\mathbf{A}$ is the right elsewhere. Many, many exciting, heartbeat-skipping discoveries follow including that Row Space of $\mathbf{A}$ is the Column Space of $\mathbf{A}^{\mbox{T}}$.
Best consumed by 2016/10/10
