Linear Dependence and Independence

This lecture covers the concepts of linear dependence and independence in vector spaces. It explains how to determine if a set of vectors is linearly dependent or independent, providing examples in different vector spaces such as R4, P(R), and M2x3(R). The instructor defines linear dependence as the existence of non-zero coefficients that form a linear combination equal to zero and linear independence as the absence of such coefficients. Various examples are given to illustrate these concepts, including sets of vectors in different vector spaces and solving equations involving linear combinations of functions.