Khan Academy on a Stick

Basic matrix operations

Keanu Reeves' virtual world in the The Matrix (I guess we can call all three movies "The Matrices") have more in common with this tutorial than you might suspect. Matrices are ways of organizing numbers. They are used extensively in computer graphics, simulations and information processing in general. The super-intelligent artificial intelligences that created The Matrix for Keanu must have used many matrices in the process. This tutorial introduces you to what a matrix is and how we define some basic operations on them.

Matrix multiplication

You know what a matrix is, how to add them and multiply them by a scalar. Now we'll define multiplying one matrix by another matrix. The process may seem bizarre at first (and maybe even a little longer than that), but there is a certain naturalness to the process. When you study more advanced linear algebra and computer science, it has tons of applications (computer graphics, simulations, etc.)

Inverting matrices

Multiplying by the inverse of a matrix is the closest thing we have to matrix division. Like multiplying a regular number by its reciprocal to get 1, multiplying a matrix by its inverse gives us the identity matrix (1 could be thought of as the "identity scalar"). This tutorial will walk you through this sometimes involved process which will become bizarrely fun once you get the hang of it.

Reduced row echelon form

You've probably already appreciated that there are many ways to solve a system of equations. Well, we'll introduce you to another one in this tutorial. Reduced row echelon form has us performing operations on matrices to get them in a form that helps us solve the system.