Kernel, Image and Linear Maps

This lecture covers the concepts of kernel and image of a matrix, denoted as ker(a) and im(a) respectively, as well as linear maps. It explains how the kernel is the set of solutions of Ax = 0, while the image is generated by the columns of A. The lecture also discusses vector subspaces, linear applications, bases of vector spaces, and the importance of linear independence. Examples are provided to illustrate these concepts, such as determining bases and canonical bases of vector spaces. The lecture concludes with a theorem on finding a basis of im(a) from a given matrix A.