# Matrices

# Matrices Introduction

Matrices. At first glance, some might say they are useless groups of numbers. Or even worse—useless groups of 1's and 0's. 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. They are 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 are a 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 more than just little old subtraction and addition. They can be multiplied, too. We pity the fool who doesn't know their matrix multiplication.

We will also go over the 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 we will learn exactly what matrices are, what their parts consist of, and how they work. You're going to know so much about matrices that there's little doubt—the neighbors will talk.