Gaussian Elimination Method

This lecture introduces the Gaussian elimination method for solving systems of linear equations by performing elementary row operations on the augmented matrix to obtain an equivalent row-echelon matrix. The method involves defining a matrix as row-echelon if it satisfies specific properties. Examples are provided to illustrate row-echelon and non-row-echelon matrices. The algorithm for Gaussian elimination is explained step by step, including exchanging rows, scaling rows, and back substitution. The lecture concludes with examples demonstrating how to determine the general solution of linear systems using the Gaussian elimination method.