Note Set 01a: Introduction to solving $\mathbf{A}\vec{x}=\vec{b}$. And happiness

How do we combine building blocks to make a structure through simple addition? Can we take an orchestral performance and separate out the instruments? In matrixology, we explore these questions through the matrix equation $\mathbf{A}\vec{x}=\vec{b}$, the mathematical representation of linear superposition for finite, discrete systems. In this introductory piece, we outline the three special pictures of the row, the column, and the matrix with a gentle 2x2 example.
Best consumed by 2016/08/29