Note Set 09a: Nullspace and Buffy the Vector Slayer

Our second of four fundamental subspaces connected to $\mathbf{A}\vec{x}=\vec{b}$ is the Nullspace of $\mathbf{A}$: All $\vec{x}$ that solve $\mathbf{A}\vec{x}=\vec{0}$. The Nullspace is the subspace of $R^{n}$ that $\mathbf{A}$ was chosen to slay, in a once-in-every-generation kind of way. We show how this special form of $\mathbf{A}\vec{x}=\vec{b}$ is crucial for solving the general $\mathbf{A}\vec{x}=\vec{b}$ problem.
Best consumed by 2016/09/26