Homogeneous Systems: Subspace Bases

This lecture focuses on finding bases for subspaces formed by the set of solutions of a homogeneous system of linear equations. The instructor explains how to determine the dimension of the space and find a base using an illustrative example. By introducing parameters, the solutions are expressed as a linear combination of vectors, highlighting their linear independence and generative properties. The process of constructing a base by setting free variables to 1 and others to 0 is demonstrated, emphasizing the importance of understanding these concepts for further study.