Linear Systems Solutions

This lecture covers the study of solutions of linear systems using the E and ER forms, including the concepts of free and basic variables, inconsistent systems, and homogeneous systems. It also delves into vector equations, recalling the geometry in R^2 and R^3, and the representation of vectors as points in space. The properties of vectors, such as addition and scalar multiplication, are discussed, along with the definition of vector equality and linear combinations. The lecture concludes with the connection between systems of equations, matrices, and vector equations.