LA17 Elementary Row Operations, Reduced Row Echelon Form, and Solving Linear Systems

Описание: What are elementary row operations? What is reduced echelon form? What is Gauss-Jordan Elimination (aka method from the Nine Chapters)? How do we use these to solve systems of linear equations? What are basic and non-basic variables? And how do we write the solutions to a system of linear equations?#linearalgebra #matrixoperations Subscribe @Shahriari for math videos at the college level.

00:00 Introduction
00:17 Goals/Plan
00:28 What is a System of Linear Equations?
01:36 What is a solution to a system of linear equations?
02:39 Progressively simpler systems
03:05 Elementary operations on equations
05:33 Augmented Matrix
06:46 Elementary row operations on a matrix
07:36 Reduced Row Echelon Form (rref) of a matrix
09:26 Gauss-Jordan Elimination aka the method from the nine chapters
11:20 Example: finding the rref of a matrix to solve a system of linear equations
15:16 Basic and Non-Basic variables
15:33 Writing the solution to a system of linear equations
16:57 Writing the solutions using set notation

This is a video in a series of lectures on linear algebra. The series is a rigorous treatment meant for students with no prior exposure to linear algebra. In this series, general vector spaces and linear transformations are emphasized.

For an annotated list of available Linear Algebra videos see
https://pomona.box.com/s/oahafa797tj5...
Linear Algebra YouTube Playlist:   • Linear Algebra, a Retro introduction  

Shahriar Shahriari is the William Polk Russell Professor of Mathematics at Pomona College in Claremont, CA USA
Shahriari is a 2015 winner of the Mathematical Association of America's Haimo Award for Distinguished Teaching of Mathematics, and five time winner of Pomona College's Wig teaching award.