In this linear algebra lesson, Gilbert Strang discusses the fundamental problem of linear algebra, which is to solve a system of linear equations. He describes three ways to look at the problem: the row picture, the column picture, and the matrix form. Strang provides examples of each method, including for a system of three equations and three unknowns, and shows that they all lead to the same solution. The lesson emphasizes the importance of understanding linear combinations, which is the most fundamental operation in the course.
The Geometry of Linear Equations -- Lecture #1. How to set up and solve matrix equations.
Gilbert Strang, 18.06 Linear Algebra, Spring 2005. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed November 16, 2008). License: Creative Commons BY-NC-SA. More info at: http://ocw.mit.edu/terms