Base of Vector Spaces

This lecture covers the concept of vector spaces, including bases, kernel, and image of a matrix. The instructor demonstrates examples to illustrate the properties of linearly dependent and independent families, as well as the extraction of a base from a generating family. The lecture also delves into the notion of coordinates systems, highlighting the importance of finding bases for vector spaces to enable computations. Through examples and explanations, the instructor guides students on how to represent vectors in different spaces using coordinates, ultimately facilitating calculations and applications in various contexts.