# Matrix Inverse by Gaussian Elimination | Linear Algebra – Dr. Ahmad Bazzi #10

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