# Algebra II: Making Matrices Work for You

A *matrix* is a rectangular array of numbers. Each row has the same number of elements, and each column has the same number of elements. Matrices can be classified as: square, identity, zero, column, and so on.

Where did matrices come from? For most of their history, they were called *arrays**.* There are references to *arrays* in Chinese, French, Italian, and many other mathematical works going back many hundreds of years. American mathematician George Dantzig’s work with matrices during World War II allowed for the coordination of shipments of supplies and troops to various locations.

Matrices are here to stay. You may be familiar with a method used to solve systems of linear equations using matrices, but this application just scratches the surface of what matrices can do.

First, just in case you’re *not* familiar with solving equations using matrices, let me give just a quick description. If you want to solve the following system of equations:

You write the matrix:

And then you perform row operations until you get the matrix:

From that matrix, you know that the solution of the system of equations is *x* = 1, *y* = –3, and *z* = –5. Pretty slick, don’t you think?

But uses for matrices don’t stop there. You can solve traffic control problems, transportation logistics problems (how much of each item to send to various distribution centers), dietary problems (how much of each food product is needed to meet several different dietary requirements), and so on. Matrices work well in graphing calculators and computer spreadsheets — just set up the problem and let the technology do all the work.