Welcome to Week 4.

This week, we will conclude our work on Chapter 1, and make a start on Chapter 2. In Wednesday’s lecture, we will have a final look at solving systems of linear equations, summarize the possible outcomes, and think about the geometric and algebraic meaning of solution sets, and how to make use of their parametric descriptions. We will also observe how elementary row operations can be understood in terms of matrix multiplication.

Here is the pre-recorded version of Lecture 7.

Slides from Lecture 7, annotated and without annotation.

Our theme in Chapter 2 is linear independence,spanning sets and bases of vector spaces. We will be back in the context of general vector spaces, but still working with matrices to represent our information. This chapter presents the central concepts that make linear algebra such a powerful environment for modelling and computation, and make vector spaces particularly amenable to analysis (compared to some other axiomatically defined structures for example).

Here is the recorded version of Lecture 8.

Slides from Lecture 8, annotated and without annotation.