This post contains notes on the MIT OpenCourseWare Linear Algebra course. Contents LECTURE 1: The Geometry of Linear Equations LECTURE 2: Elimination with Matrices 2.1 Example Equations 2.2 Elimination 2.3 Back-Substitution 2.4 Matrices Multiplication LECTURE 1: The Geometry of Linear Equations Ax is a combination of the columns of A. $$ A = \begin{bmatrix} 2 & 5 \\ 1 & 2 \end{bmatrix}, x = \begin{bmatrix} 1 \\ 2 \end{bmatrix} $$