Matrix Equations: Linear Combinations and Solutions

This lecture covers the concept of matrix equations, focusing on linear combinations and solutions. Starting with the definition of the part generated by a set of vectors, the instructor explains how to express solutions of homogeneous and non-homogeneous systems. The lecture also delves into the conditions under which a matrix equation admits a solution and how to calculate matrix-vector products. Demonstrations and theorems are presented to illustrate key concepts, such as the equivalence between matrix and vector equations. The lecture concludes with examples showcasing linear combinations of columns in a matrix.