Welcome to Week 3.

Our first lecture this week will conclude the discussion of systems of linear equations, and start to review the algebra of matrices.

Slides for Lecture 5.

In Lecture 6, we will look at some other features of matrix algebra, such as matrix-vector multiplication, and matrix multiplication. We will think about interpretations of the meaning of matrix multiplication in different contexts, starting with tables of data. We start to consider matrix multiplication as composition of linear transformations, and continue with that theme in Week 4.

Slides for Lecture 6.

Here are some video lectures from last year, with some of the content that we will discuss in Lectures 5 and 6 this year. Please note that the content is organised slightly differently this year and not in the same order, so the match with the video backup is not exact.

## Weekly Challenge 1

The first weekly challenge is to give an example similar to Example 1.3.7 on page 14 of the lecture notes, of some “realistic” scenario where matrices arise as records of data, and a matrix product makes practical sense. Please upload your example via the Blackboard assignment, by Friday February 3.

For full marks, your example needs to be original (not a copy from a website or a tiny adaptation of the one in the lecture notes), and it needs to be presented carefully, with a focus on explaining to a reader about the significance of matrix multiplication. Think of writing something that would have helped you to understand this topic, if you had read it in the first place.