Linear Dependence Theorems and Proofs

This lecture covers the concept of linear dependence, the theorem stating that if a vector is a solution of a system, then the set of vectors of the form p + h, where h is a solution of another system, is also a solution. The lecture also discusses linear independence, showing that a family of vectors is linearly independent if the vector equation admits only the trivial solution. The instructor illustrates these concepts with examples and proofs, emphasizing the importance of understanding linear dependence in linear algebra.