Dimension: Bases and Extraction of a Base

This lecture covers the concept of dimension in linear algebra, focusing on vector spaces of finite dimension. It explains examples of vector spaces such as R₂, P₂(R), and Mmxn(R). The extraction of a base from a generating set is discussed, along with the completion of a free set to form a base. The proof involves determining if a set is linearly independent or dependent, and how to find a base from it. Examples are provided to illustrate the concepts, including finding bases and generating sets in specific vector spaces.