Linear Applications: Kernel-Image Theorem

This lecture covers the Kernel-Image Theorem in linear algebra, stating that for a linear application with a finite-dimensional vector space, the dimension of the domain equals the sum of the dimensions of the kernel and the image. It also explores the conditions for bijectivity and the dimension of the space of mappings. Additionally, it discusses linear forms, their properties, and the concept of surjectivity. The lecture concludes with a detailed explanation of how to determine if an application is injective or surjective.