Linear Algebra: Matrix Operations and Basis

This lecture covers topics related to matrix operations, such as determining the rank of a matrix, finding the kernel dimension, and working with transposed matrices. The instructor explains how to calculate the rank and kernel dimension of a matrix, emphasizing the importance of bases and linear independence. The lecture also delves into finding coordinates of vectors in different bases, transforming linear transformations into matrices, and completing bases to form a full vector space. Practical exercises are provided to reinforce the understanding of these concepts.