### Learning Outcomes

By the end of this section, you will be able to:

- Identify and define the properties of real numbers

This module introduces the matrix: a mathematical tool that may be brand new to you. We can use matrices to solve systems of linear equations, but there are much more to these powerfully efficient constructions. Matrix applications can be found in nearly every scientific field. They are used heavily in statistics, physics, electrical engineering, and computer science, to name a few. A deeper exploration of matrices and matrix operations appears in Linear Algebra, a branch of mathematics that is fundamental to nearly all mathematical areas.

In this module, you’ll learn how to perform operations on matrices to combine them and scale them by a numerical multiplier. You’ll also learn how to find and use the inverse of a matrix and how to use matrices to solve a linear system.

Before studying the properties of matrix operations (sums, differences, products, inverses, and identity) you should refresh your understanding of the properties of real numbers. Though matrix operations work a little differently than operations on real numbers, refreshing the terminology will be helpful.

Warm up for this module by refreshing important concepts and skills you’ll need for success. As you study these review topics, recall that you can also return to Algebra Essentials any time you need to refresh the basics.

### Recall for success

Look for red boxes like this one throughout the text. They’ll show up just in time to give helpful reminders of the math you’ll need, right where you’ll need it.