Linear Application Image and Rank

This lecture covers the image of a linear application and its rank in the context of linear algebra. It defines the image of an application as the set of all outputs, discusses the rank of the image, and proves that the image is a subspace of the codomain. The lecture also explores examples and remarks on the kernel and image of a linear application, emphasizing the relationship between their dimensions and the rank of the application. Various propositions are presented to illustrate the properties of the image of a linear application. Additionally, examples of linear transformations are provided to enhance understanding.