But matrix algebra goes far, far beyond that. We can generalize to three dimensions (find the point or line of intersection of three planes in space), or even to four or more dimensions – dimensions we can't even conjure in our 3-D minds.

Using matrix algebra, we can reduce a four dimensional (4 equations, 4 unknowns) problem like this:

to the matrix & vector equation below. You don't need to know what these symbols mean right now. That's what the following sections will cover. Just notice the relative simplicity of the notation:

It might not look any simpler to solve written that way, but in time you'll learn that such problems can be much simpler to solve when expressed as matrix equations, and matrices will lead to so much more.

*OK, they might be parallel, in which case they won't have a point of intersection, or they might be the same line, in which case the number of intersection points will be infinite ... but you get the idea.

Matrix algebra is used heavily in

• Fields where keeping track of large blocks of data is important, like the insurance industry
• Large database and sorting operations, like indexing and searching the internet
• Solving complicated differential equations – in quantum mechanics, for example
• Matrices (plural of matrix) are used to "operate" on vectors to produce the rotations and scaling transformations needed to render images, such as those in video games
• Matrices like "tensors" are important for describing complex motions like a rotating body rotating on a rotating body (boom - mind blown)
• ... and many other applications

As you study them, matrices will take on much more meaning than simply a block of numbers that are the coefficients of unknowns in a system of linear equations. And those systems will take on deeper meanings, too.

The index below should help you navigate the matrix pages. If you don't know very much about matrices, it's probably best to start at the beginning.