The Geometry of Linear Equations

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Taught by OCW
  • Currently 4.0/5 Stars.
10731 views | 1 rating
Lesson Summary:

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.

Lesson Description:

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), (Accessed November 16, 2008). License: Creative Commons BY-NC-SA. More info at:

Additional Resources:
Questions answered by this video:
  • What is Linear Algebra?
  • What are linear combinations?
  • Staff Review

    • Currently 4.0/5 Stars.
    A good introductory lecture to Linear Algebra. This video explains how to think about linear combinations of column matrices geometrically. If you are having trouble understanding what it means to solve a system of linear equations in Linear Algebra, check out this video first.