Gauss-Jordan Method

This lecture covers the Gauss-Jordan method for solving systems of linear equations. It explains the theorem stating that a system of linear equations has either no solution, one solution, or infinitely many solutions. The method involves reducing the augmented matrix associated with the system to row-echelon form and then further reducing it to reduced row-echelon form. The lecture also discusses the concept of reduced row-echelon matrices and provides examples to illustrate the process. Additionally, it explores the case when a system has a unique solution and compares the efficiency of the Gauss-Jordan reduction method with the backward substitution method. The lecture concludes with examples demonstrating how to determine the general solution of linear systems.