Chapter 05 If the Inverse of A Exists is it Unique

System of Equations (CHAPTER 5)

Topic

If the inverse of $\left[ A \right]$ exists, is it unique?

Summary

Learn how to prove that if the inverse of $\left[ A \right]$ exists, then it is unique.

Learning Objective

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

Transcript

Read the transcript

All Videos for this Topic

- - A real life problem of setting up simultaneous linear equations [YOUTUBE 5:23]
  - Writing simultaneous linear equations in matrix form [YOUTUBE 5:25]

- - Consistent and inconsistent system of equations Theory [YOUTUBE 2:56]
  - Consistent and inconsistent system of equations Example [YOUTUBE 5:31]

- - Rank of a matrix Definition [YOUTUBE 1:21]
  - Rank of a matrix Example 1 [YOUTUBE 1:31]
  - Rank of a matrix Example 2 [YOUTUBE 2:50]

- - Distinguishing between consistent and inconsistent system of equations based on rank of matrices [YOUTUBE 3:06]
  - Distinguishing between consistent and inconsistent system of equations based on rank of matrices Example 1 [YOUTUBE 4:15]
  - Distinguishing between consistent and inconsistent system of equations based on rank of matrices Example 2 [YOUTUBE 8:42]
  - Distinguishing between consistent and inconsistent system of equations based on rank of matrices Example 3 [YOUTUBE 6:07]

- - If a solution exists, how do we know if it is unique? [YOUTUBE 3:25]
  - Does a set of equations have a unique solution? Example 1 [YOUTUBE 2:18]
  - Does a set of equations have a unique solution? Example 2 [YOUTUBE 2:23]
  - If we have more equations than unknowns, does it mean we have inconsistent system of equations? [YOUTUBE 8:11]
  - Can a system of equations have more then one but not infinite number of solutions? [YOUTUBE 4:57]

- - Can we divide two matrices? [YOUTUBE 5:39]
  - Some statements about the inverse of matrices [YOUTUBE 2:53]
  - Inverse of matrices Example [YOUTUBE 3:40]
  - Using concept of inverse to solve a set of equations [YOUTUBE 2:27]
  - Finding the inverse of a matrix Theory [YOUTUBE 4:32]
  - Finding the inverse of a matrix Example [YOUTUBE 7:03]
  - Finding the inverse of a matrix by adjoints Theory [YOUTUBE 2:15]
  - Finding the inverse of a matrix by adjoints Example [YOUTUBE 7:19]
  - If the inverse of [A] exists, is it unique? [YOUTUBE 2:30]

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.