Column Rank and Systems of Equations

This lecture covers the concept of column rank and its relation to systems of equations in linear algebra. It explains how to represent a system of equations using matrices, specifically the coefficient matrix and the augmented matrix. The lecture also delves into finding solutions for systems of equations by analyzing the column space of the coefficient matrix. Examples are provided to illustrate the concepts discussed, including determining the column rank and the dimension of the column space. Additionally, the lecture explores the relationship between the column space of a matrix and the solutions to the corresponding system of equations.