ABSTRACT
Linear Algebra is the discipline that studies systems of linear equations, vector spaces, and linear transformations. In its simplest form, systems of linear equations allow us to find if and where two lines in the plane intersect and how to view points in the plane as two-dimensional vectors, something you have likely already seen in high school. Matrix algebra and vectors spaces help us find and study the solutions of linear systems of several variables and their properties, as well as answer questions about sets of multi-dimensional vectors of real numbers and their characteristics. Linear transformations are special kind of functions between vector spaces that preserve their essential properties. In particular, they are used to prove that every abstract vector space “generated” by a finite number of vectors behaves mathematically the same way as a space of vectors of real numbers. Further, some important questions about linear transformations can be translated into questions about vector spaces linked with matrices and can be answered using systems of linear equations.
