Linear Equations: Consistency and Solutions

This lecture covers the determination of consistency and general solutions of linear equation systems. It explains the theorem stating that such systems have either no solution, a unique solution, or an infinite number of solutions. The lecture also discusses operations like exchanging equations, multiplying by a non-zero number, and replacing equations to find the general solution. Examples are provided to illustrate the concepts, including the use of matrices to represent linear systems and the process of obtaining the augmented matrix. The lecture concludes with the concept of equivalent matrices obtained through elementary row operations.