Matrix Equations: Linear Combinations

This lecture introduces the concept of matrix equations as linear combinations of columns, illustrating how to find solutions and interpret them geometrically. It covers the definition of vector spaces, span, and linear combinations, providing insights into the geometric interpretation of vector spaces. The lecture also explains the rule of 'row-column' for matrix-vector multiplication and the geometric interpretation of vector spaces. Additionally, it discusses the properties of matrix equations, including the existence of solutions and the geometric interpretation of solutions. The lecture concludes with examples demonstrating how to find the equation of a plane spanned by given vectors.