Overview:

1. Introduction to matrices
2. Adding and subtracting matrices
3. Multiplying matrices
4. 2 × 2 Matrices and linear transformations
5. Determinants of 2 × 2 matrices
6. Inverses of 2 × 2 matrices
7. Invariant points and lines in 2 dimensions
8. 3 × 3 Matrices and linear transformations
9. Determinants of 3 × 3 matrices
10. Inverses of 3 × 3 matrices
11. Matrices and simultaneous equations

A matrix is an array of elements. The elements we will see in matrices will usually be numbers or algebraic expressions. An \(m \times n\) matrix has \(m \) rows and \(n \) columns. In some books, you will find matrices written in square brackets [also known as box brackets], but here we will use round brackets (also known as parentheses). Matrices are denoted by bold, capital letters e.g. A.

The order of a matrix tells you how many rows and columns it has. Therefore, \( \begin{pmatrix} 5 & 2 & 4 \\ 1 & 8 & 2 \\\end{pmatrix}\) is simply a \(2 \times 3\) matrix.