INTRODUCTION TO MATRIX ALGEBRA

Transforming Matrix Algebra for the STEM Undergraduate

 

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SYSTEM OF EQUATIONS (CHAPTER 5)

 

If the inverse of [A] exists, is it unique?

By Autar Kaw



TOPIC DESCRIPTION
 

Learn to prove that if the inverse of [A] exists, then it is unique.

 

This video teaches you to prove that if the inverse of [A] exists, then it is unique.


ALL VIDEOS FOR THIS TOPIC
 

A real life problem of setting up simultaneous linear equations [YOUTUBE 5:23] [TRANSCRIPT]

Writing simultaneous linear equations in matrix form  [YOUTUBE 5:25] [TRANSCRIPT]

 

Consistent and inconsistent system of equations Theory [YOUTUBE 2:56] [TRANSCRIPT]

 

Consistent and inconsistent system of equations Example [YOUTUBE 5:31] [TRANSCRIPT]

 

Rank of a matrix Definition [YOUTUBE 1:21] [TRANSCRIPT]

Rank of a matrix Example 1 [YOUTUBE 1:31]  [TRANSCRIPT]

Rank of a matrix Example 2  [YOUTUBE 2:50]  [TRANSCRIPT]

 

Distinguishing between consistent and inconsistent system of equations based on rank of matrices [YOUTUBE 3:06] [TRANSCRIPT]

Distinguishing between consistent and inconsistent system of equations based on rank of matrices Example 1 [YOUTUBE 4:15]  [TRANSCRIPT]
Distinguishing between consistent and inconsistent system of equations based on rank of matrices Example 2  [YOUTUBE 8:42]  [TRANSCRIPT]

Distinguishing between consistent and inconsistent system of equations based on rank of matrices Example 3 [YOUTUBE 6:07]  [TRANSCRIPT]

 

If a solution  exists, how do we know if it is unique?  [YOUTUBE 3:25]  [TRANSCRIPT]

Does a set of equations have a unique solution? Example 1  [YOUTUBE 2:18] [TRANSCRIPT]

Does a set of equations have a unique solution? Example 2 [YOUTUBE 2:23]  [TRANSCRIPT]
If we have more equations than unknowns, does it mean we have inconsistent system of equations?  [YOUTUBE 8:11]  [TRANSCRIPT]

Can a system of equations have more then one but not infinite number of solutions?  [YOUTUBE 4:57] [TRANSCRIPT]

 

Can we divide two matrices?  [YOUTUBE 5:39]  [TRANSCRIPT]
Some statements about the inverse of matrices  [YOUTUBE 2:53]  [TRANSCRIPT]

Inverse of matrices Example  [YOUTUBE 3:40]  [TRANSCRIPT]

Using concept of inverse to solve a set of equations  [YOUTUBE 2:27]  [TRANSCRIPT]

Finding the inverse of a matrix Theory [YOUTUBE 4:32] [TRANSCRIPT]

Finding the inverse of a matrix Example  [YOUTUBE 7:03]  [TRANSCRIPT]
Finding the inverse of a matrix by adjoints Theory  [YOUTUBE 2:15]  [TRANSCRIPT]

Finding the inverse of a matrix by adjoints Example  [YOUTUBE 7:19] [TRANSCRIPT]

If the inverse of [A] exists, is it unique?  [YOUTUBE 2:30]  [TRANSCRIPT]


COMPLETE RESOURCES
  Get in one place the following: a textbook chapter, a PowerPoint presentation, individual YouTube lecture videos, multiple-choice questions, and problem sets on System of equations.

Copyrights: University of South Florida, 4202 E Fowler Ave, Tampa, FL 33620-5350. All Rights Reserved.

Questions, suggestions or comments, contact kaw@usf.edu 

This material is based upon work supported by the National Science Foundation under Grant# 0126793, 0341468, 0717624,  0836981, 0836916, 0836805, 1322586.  Any opinions, findings, and conclusions orCreative Commons License recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.  Based on a work at http://mathforcollege.com/ma.  Introduction to Matrix Algebra is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.