Lecture
This lecture continues the exploration of the Rank Theorem in the context of linear applications, focusing on consequences such as the relationship between the dimensions of the domain, kernel, and image of a linear transformation. Through examples involving mappings between vector spaces and matrices, the instructor illustrates how to determine if a linear transformation is injective or surjective based on the dimensions of its kernel and image. The lecture also covers the application of the Rank Theorem to polynomial spaces, showcasing how to analyze the injectivity and surjectivity of polynomial transformations.