Gaussian elimination is an algorithm for solving problems, that is, systems of linear equations. Gaussian elimination is very commonly introduced in introductory textbooks on algebra and differential equations, and many of you probably have experience using it to solve small systems of equations by hand on paper.

However, this is a very old-fashioned viewpoint. Nowadays, instead of doing Gausian elimination on paper, we do LU decomposition on a computer (the two are closely related). In this course we review Gaussian elimination only as a pathway towards understanding the LU decomposition.

Some online resources on Gaussian elimination

• Wikipedia. Examples, history, applications, efficiency, pseudocode.
• Wolfram Alpha. Quite a nice explanation with a concrete example.