Linear Algebra: Applications and Spaces

This lecture covers the concept of linear applications in general, focusing on applications that respect specific conditions. It discusses the properties of matrices, such as uniqueness and determinants, and explores vector subspaces generated by linear transformations. The lecture also delves into the rank of matrices, the kernel of linear applications, and the resolution of 3x3 linear systems. Through examples and proofs, the instructor illustrates the theoretical concepts with practical applications, emphasizing the importance of understanding linear algebra in various mathematical contexts.