Linear Equations: Solving Systems and Matrices

This lecture introduces the fundamental concepts of linear equations, focusing on solving systems with zero, one, or infinite solutions. The instructor explains how to manipulate equations to triangular form and demonstrates the process using matrices. By applying operations on augmented matrices, students learn to solve systems efficiently and verify solutions. The lecture emphasizes the importance of verifying solutions and introduces the concept of matrices as a powerful tool for solving linear equations. Through step-by-step examples, students gain a solid understanding of how to apply matrix operations to solve systems of linear equations.