Linear Applications: Bases and Dependencies

This lecture covers the concept of finding a basis of the image of a linear application using invertible matrices and canonical bases. It explores forming bases for different spaces, identifying linear dependencies, and extracting bases from families of vectors. The lecture also delves into the relationships between pivot columns, linear combinations, and the reduced matrix. Additionally, it discusses the importance of the order of vectors in a base and demonstrates how to find bases for the kernel and image of a linear transformation.