Elementary Linear Algebra with Applications, Custom for University of California, Berkeley, Math 54

From Introduction To Linear Equations And Matrices: Systems of linear equations have many applications. They are found in economics, social sciences, and medicine as well as the biological and physical sciences and mathematics. The method we will use to solve such systems is called Gaussian elimination, after Carl Friedrich Gauss (1977-1855), one of the most prolific mathematicians in history. However, the method was known well before Gauss; indeed it appeared in Chinese text, Chui-chang Suan-shu, around 250 B.C. We study this method not only because it has historical significance but also because it is the basis for the best direct methods for programming a computer to solve linear systems. Equally important, the mathematical study of this method opens the door to a fascinating and widely applicable branch of mathematics, linear algebra.