# Solving Ax = b: Row Reduced Form R

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Lesson Summary:

In this linear algebra lesson, you will learn how to solve linear equations of the form AX = B by using row reduced echelon form (rref). The first step is to identify whether or not the system has a solution by elimination, and if so, whether there is only one solution or a family of solutions. After finding one particular solution, you can add on any vector from the null space to get the complete solution. The null space is a subspace that consists of all combinations of special solutions that have a zero right-hand side.

Lesson Description:

Solving Ax = b: Row Reduced Form R -- Lecture 8. Learn how to solve equations that look like Ax = b using row reduced echelon form (rref).

Gilbert Strang, 18.06 Linear Algebra, Spring 2005. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed November 19, 2008). License: Creative Commons BY-NC-SA.

• How do you solve Ax = b?
• What is row reduced echelon form?
• What is rref?
• When does Ax = b not have a solution?
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• Currently 4.0/5 Stars.
This video explains how to find the solution to a matrix equation Ax = b, and to determine when there will not be a solution. The process used in this video is elimination to get to row reduced echelon form.
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