Gaussian elimination, a.k.a row-reduction, is a technique used to solve systems of linear equations. Given a system Ax = b, the coefficients of the matrix A along with vector b are stacked next to each other [ A | b ] to form the so-called Augmented matrix. Then, using an appropriate sequence of row-operations, we can reduce the augmented matrix to an upper-triangular one to solve in a backward manner. The lecture is outlined as follows:

00:00 What does Gaussian Elimination do ?

01:12 Upper Triangular Matrix

02:38 Why do we perform Gaussian Elimination ?

03:16 BackSolving: Solving by back-substitution

05:21 The Gaussian Elimination Procedure

09:06 Example on the Gaussian Elimination Procedure

13:40 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

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

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