Linear Algebra: Associated Matrix and Subspaces

This lecture covers the concept of the matrix associated with a linear map, including forming bases for the image and kernel spaces. It explains the process of finding the kernel by reducing the matrix and the relationship between the image and kernel spaces. The lecture also discusses the properties of injective and surjective applications, as well as the rank theorem. Through examples and demonstrations, students learn how to determine pivot columns, establish bases, and understand the linear transformations between vector spaces.