Matrix Rank: Row-Column Rank Relationship

This lecture concludes the topic of matrix rank by exploring the relationship between the row rank and column rank of a matrix. The instructor explains how the column rank of a matrix is equal to the row rank of its transpose, illustrating this concept with examples and calculations. The lecture also covers the concept of linearly independent vectors and how it relates to the rank of matrices, providing insights into the dimensionality of column spaces. Additionally, the instructor introduces the notion of a base for the column space of a matrix, emphasizing its importance in understanding the structure of vector spaces.