Matrix Multiplication

This article is a work in progress.

Matrix multiplication is.. a bit confusing. But only at first!

Let’s start off the same way I was originally taught by maths tutor - with this exact example.

A salesperson sells items of three types I, II, and III, costing €10, €20, and €30. The table will show how many items of each type are sold on Monday morning and afternoon.

	Type I	Type II	Type III
Morning	3	4	1
Afternoon	5	2	2

Let’s convert this table into the matrix $A$:

$\left(\begin{array}{ccc}3& 4& 1\\ 5& 2& 2\end{array}\right)$

We will take $B$ to be a 3x1 matrix containing the price of the items, like so:

$B=\left(\begin{array}{c}10\\ 20\\ 30\end{array}\right)$

Remember: $B$ is a column vector - Please see Introduction to Matrices.

Now, $C$ is a 2x1 matrix (another column vector) whose entries are the total income from the morning and afternoon sales.

$C=\left(\begin{array}{c}140\\ 150\end{array}\right)$

Lost?

The values are from the total incomes, so the 140 comes from $(3\ast 10)+(4\ast 20)+(1\ast 30)$