To compute the inverse, attach the n columns of the identity matrix to form an augmented matrix. By performing elementary row operations on the entire augmented matrix, reduce the coefficient matrix portion to upper-triangular form. Perform back substitution once for every attached column that was produced from the identity matrix. The solution obtained from the original right-hand side [1 0 .. 0] is the first column of the inverse. Continue in the same fashion to obtain columns 2 − n of the inverse.

This lecture is outlined as follows:

00:00 Intro

01:02 Key Representation

02:01 How it works

05:39 Example 1: Invertible Matrix

10:37 Example 2: Non-invertible Matrix

12:44 Summary

Lecture 1: Matrix Arithmetic https://youtu.be/qX_pH-3HiW8

Lecture 2: Linear Transformations https://youtu.be/uj-GlQc8ijw

Lecture 3: Powers of Matrices with Application to Graph Theory https://youtu.be/Xv1rkvcnaa4

Lecture 4: Non-Singular Matrices and Linear Systems https://youtu.be/uqRt55cOa84

Lecture 5: Matrix Transpose and Symmetric Matrices https://youtu.be/fl785R8ftFU

Lecture 6: Introduction to Linear Systems https://youtu.be/Jk2qWR2SX0c

Lecture 7: Solving Square Linear Systems https://youtu.be/oeFxaGitlUU

Lecture 8: Gaussian Elimination https://youtu.be/3dDbelcKD7o

Lecture 9: Systematic Solution of Linear Systems https://youtu.be/Hzwx2H7L-S4

https://www.youtube.com/c/AhmadBazzi

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