Vetores e transformações lineares no plano

Abstract

This dissertation aims to conceptualize mathematical functions in detail, exploring the injector, subjective, composite and inverse functions. Then, it approaches the concept of geometric vector and its transition to algebraic form, with focus on vectors on the Cartesian plane, performing operations with vectors on the plane and the validity for their properties. Matrices also were highlighted, validating their operations with some properties, and thus forward to the understanding of vector spaces with their operations. Finally, define linear transformations and some plane transformations are presented, linear or not, such as rotation, reflection, elongation, shear and translation, all with a simple and accessible language, full of illustrated examples that show how to determine each one of these transformations.