# Matrices and Determinants

By M Bourne

## Introduction

Why study Matrices?

A **matrix** is simply a set of numbers arranged in a rectangular table.

Shown is an example of a 2 × 4 matrix. It has 2 rows and 4 columns. We usually write matrices inside parentheses ( ) or brackets [ ].

We can add, subtract and multiply matrices together, under certain conditions.

We use matrices to solve simultaneous equations, that we met earlier.

Matrices are used to solve problems in:

- electronics
- statics
- robotics
- linear programming
- optimisation
- intersections of planes
- genetics

We see several of these applications throughout this chapter, especially in Matrices and Linear Equations.

For large systems of equations, we use a computer to find the solution. This chapter first shows you the basics of matrix arithmetic, and then we show some computer examples (using Scientific Notebook and LiveMath) so that you understand what the computer is doing for you.

You can skip over the next part if you want to go straight to matrices.

## Determinants

Continue reading below ⇩

A **determinant of a matrix** represents a single number. We obtain this value by multiplying and adding its elements in a special way. We can use the determinant of a matrix to solve a system of simultaneous equations.

For example, if we have the (square) 2 × 2 matrix:

The determinant of this matrix is written within vertical lines as follows:

We'll see in the next section how to evaluate this determinant. (It has value -29).

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Chapter Contents

- Matrices and Determinants
- 1. Determinants
- Systems of 3x3 Equations interactive applet
- 2. Large Determinants
- 3. Matrices
- 4. Multiplication of Matrices
- 4a. Matrix Multiplication examples
- 4b. Add & multiply matrices applet
- 5. Finding the Inverse of a Matrix
- 5a. Simple Matrix Calculator
- 5b. Inverse of a Matrix using Gauss-Jordan Elimination
- 6. Matrices and Linear Equations