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
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