Study Guide


Matrices Introduction

Matrices. At first glance, some might say they're just useless groups of numbers. Or even worse—useless groups of 1s and 0s. For those of us who don't speak fluent binary, why should we learn them? Because life is complicated, and it sometimes throws more than one or two or—gulp—even three variables at us. A matrix is a helpful way to keep things organized. Just ask Keanu Reeves.

The real question is, do you want to swallow the blue pill and continue along, blissfully ignorant about matrix operations? Or are you ready to swallow the red pill with us?

A matrix is, generally, a group of numbers or variables arranged in a rectangle. Each row has the same number of inputs, and each column also has the same number of inputs. If it's a square matrix, then the columns and rows each have the same number of inputs. Oh, rectangles and squares…that really takes us back.

Matrices are useful because they give us a simple way to put a series of data points together. If you're doing inventory at A & F, you might need a matrix to assess how many shirts you have, what kind, what size, and so on. If you don't learn about matrices, you could be stuck at A & F for life.

We'll start with the nuts and bolts of the matrix: matrix addition, matrix subtraction, and Cramer's Rule. We're not talking about Seinfeld, either. We will then continue to follow the white rabbit and see what we find. We'll see that there's more a matrix can handle than just little old subtraction and addition. They can be multiplied, too. We pity the fool who doesn't know their matrix multiplication.

We'll also go over scalar multiplication and multiplying two matrices together. We'll even get all fancy-pants and multiply matrices with different dimensions. Don't even get us started on the identity matrix; who does it think it is?

In this unit, you'll learn exactly what matrices are, what their parts consist of, and how they work. You'll be the ruler of Matrix Mountain in no time, wielding your power with an iron fist.

Matrices Resources

Tools and Games

Web 2.0 Scientific Calculator
For when your solar-powered calculator isn't enough.

Matrix Calculator
Here's a good way to double-check your work.


Matrix History
The moldy old history of matrices.

PurpleMath on Matrix Size
What is an augmented matrix, anyways? Find out here.


The Red Pill Science
In case you've never seen what we're talking about.

Introduction to Matrices.
A solid intro to matrices from a dude with a radio-announcer voice.

Multiplying Matrices
Go back to the old-fashioned pen-and-paper method.

MIT Lecture
They know math like it's no one's business.