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.