Linear Algebra: Rank Theorem

This lecture covers the Rank Theorem in linear algebra, focusing on the concept of rank, kernel, and image of a matrix. It explains how to calculate the rank of a matrix and its relationship with the dimensions of the kernel and image. The lecture also delves into determinants for square matrices, discussing properties and generalizations. The instructor demonstrates the application of the Rank Theorem through examples and proofs, emphasizing the importance of understanding the fundamental concepts of linear algebra.