Vector Spaces: Definitions and Properties

This lecture covers the definition of vector spaces and their properties, including the ten axioms that must be satisfied for a set to be considered a vector space. It also discusses subspaces of vector spaces, showing that a subset is a subspace if it satisfies two conditions. Examples are provided to illustrate the concepts, such as determining if specific sets are subspaces or not. The lecture concludes with a discussion on linear combinations of vectors and how to determine if a vector is a linear combination of other vectors.