Foundations of Linear Algebra

This section serves as foundational preparation for the study of abstract vector spaces. Here, we undertake a detailed examination of two principal themes: vector geometry and the solution of linear equations, together with the associated methods of matrix analysis. We demonstrate how the structures and operations of linear algebra emerge naturally from these concrete, historically motivated settings. While it may seem efficient to proceed directly to the abstract treatment of linear algebra, it is strongly recommended that students engage thoroughly with this material first. Doing so cultivates a deeper, more intuitive understanding of the core concepts that underpin the subsequent abstract theory.