Linear Equations and Vector Spaces

This lecture continues the study of linear equations and vector spaces, focusing on defining Rn as the set of all vectors with n components and generalizing the concept to include vector addition and scalar multiplication. The lecture explores the structure of Rn, introduces the concept of linear combinations, and discusses the span of vectors. Through examples and algebraic explanations, the instructor illustrates how to determine if a system of linear equations has a solution and how to represent it using matrices. The lecture also covers matrix-vector multiplication and the conditions for a system to have a unique solution.