Resumen

This work aimed to characterize the presentations and representations of the Linear (In) dependence objects, Generators, Base and Dimension in a vector space contained in three linear algebra books from the 70's, in which Guilherme de La Penha appears as an author or co-author. From Chaquiam (2012), the books Linear Algebra I and II (1974), Synopsis of Linear Algebra (1975) and Introduction to Linear Algebra (1977) were highlighted. Support was sought in documentary research with the help of Bardin's Content Analysis Theory (2016), which in turn enabled the creation of the following categories of analysis of these books: (i) Introduction to the content; (ii) Definition of the mathematical object and (iii) Use of different representations of the mathematical object. From the analysis it was possible to list the outstanding characteristics of these books in relation to the mathematical objects considered in the initial questioning, among which, the use of numerical ideas and other concepts as supports to the definitions of the objects, as well as the concern with maintaining rigor of the mathematical text. In addition, at least three types of representations of mathematical objects were identified in the analyzed books: natural language representation, algebraic representation and geometric representation. In general, it was observed that the authors intended to make the linear algebra content clearer, in order to contribute to the understanding of these mathematical objects in a complete way in several aspects, among them, the numeric, the algebraic and the geometric, without losing sight of formalization and mathematical rigor.