Welcome to Week 2.

Our topic this week is the development of a systematic method to find all solutions of a system of linear equations. A solution of a system of linear equations is a set of values for the variables that simultaneously satisfies all of the equations in the system. We will encode the system of equations as a matrix, and apply the technique of Gauss-Jordan elimination to simplify the matrix to a form where the solution can be easily read.

In Lecture 3 (Wednesday) we look at how to solve a system of equations using *elementary row operations* to reduce the *augmented matrix* to *row echelon form*.

Here is the pre-recorded version of Lecture 3.

Slides from Lecture 3, annotated and without annotation.

In Lecture 4 (Friday), we define the *reduced row echelon form* and the method of *Gauss Jordan elimination*, and we will look at the different possible outcomes that can arise when solving a system of linear equations.

Here is a recording corresponding (roughly) to Lecture 4.

The relevant section of the lecture notes this week is Section 1.3.