Linear Algebra: Bases and Dimension

This lecture covers the concept of bases and dimension in linear algebra, focusing on the calculation of vector spaces generated by given sets of vectors. It also explores the intersection of vector spaces and the determination of dimensions. The lecture delves into solving problems related to list generators and determining the bases of solution spaces in homogeneous systems. Additionally, it discusses the properties of subspaces and the relationships between their dimensions. The lecture concludes with exercises on finding bases for the kernel and column space of matrices, emphasizing the importance of understanding bases in linear algebra.