ABSTRACT
Linear algebra encompasses many topics but, at the introductory levels, it studies solution sets to systems of linear equations in multiple variables. This theory has applications in many branches of mathematics, in computer science, and in the natural and social sciences. The structures introduced in solving systems of linear equations generalized to the theory of vector spaces, and motivated the concepts of linear transformation, kernel, image, subspaces, and so on. However, the study of solving linear equations in multiple variables could also be generalized in a different direction, namely the study of systems of polynomial equations in multiple variables.
