Matrix Equations and Homogeneous Systems

This lecture covers matrix equations, homogeneous systems of linear equations, and their solutions. It explains the relationship between matrix equations and vector equations, the existence of solutions, and how to determine if a system is consistent. The lecture also delves into the properties of homogeneous systems, the concept of trivial and non-trivial solutions, and the conditions under which a homogeneous system has non-trivial solutions. Examples are provided to illustrate the theoretical concepts discussed.