This textbook discusses vector spaces, linear maps and matrices, determinants, eigenvectors, and eigenvalues in addition to linear systems and the Gauss' technique. Three or four talks on related subjects and applications are included in each chapter.
It includes the necessary information and supports all of the findings, but it does not begin by supposing that kids are adept at abstract work. Instead, it moves forward with a ton of motivation, lots of computational examples, and tasks that range from simple checks to a few difficult ones. The objective is to increase each student's degree of mathematical maturity within the context of generating the material for an undergraduate course.