Linear Dependence and Independence

This lecture covers the concepts of linear dependence and independence of vectors, including the generation of subspaces, corollaries related to linear dependence, and examples illustrating linear independence. The instructor explains how to determine if a set of vectors is linearly dependent or independent, and how to extract a base from a set of vectors. The lecture also delves into the theorem of the extracted base, showcasing the process of extracting a base from a set of vectors. Various examples are provided to demonstrate the application of these concepts in vector spaces and polynomial spaces.