Linear Independence in Vector Spaces

This lecture covers the concept of linear independence in vector spaces, where a set of vectors is considered linearly independent if no vector in the set can be expressed as a combination of the others. It also discusses the criteria for determining linear independence, such as the linear (non-trivial) combination of vectors that reduces to the zero vector. The lecture further explores the notion of bases in vector spaces, defining a base as a set of vectors that is both linearly independent and spans the vector space. Additionally, it delves into the properties of bases, including their finite nature and the relationship between the dimension of a vector space and the number of elements in a base.