The present study aimed to investigate how the historical development of the concepts
of Linear Dependence and Independence can be approached in Linear Algebra
courses to enable a better understanding of these concepts by Mathematics
undergraduates. To this end, we developed a Bibliographic Research with a qualitative
approach for data analysis consisting of two moments. In the first moment, based on
Dorier (1995b; 2000) and Moore (1995), we discuss the historical constitution of Linear
Algebra, in which we identify four different preceding notions of the current concepts
of Linear Dependence and Independence, whether they are inclusive dependence
(Euler), unified dependence for equations and n-tuples (Frobenius), generalization of
dependence to n-dimensional space (Grassmann) and axiomatization of dependence
and linear independence (Peano). In the second moment, we present didactic
suggestions, based on Mendes (2006; 2015; 2016) and Brandemberg (2018; 2021),
on how to approach these different notions in Linear Algebra courses. Such
suggestions aim to give students the opportunity to have contact with different aspects
that allow them to broaden their understanding of linearity as a relationship between
vectors, as well as to visualize the current definitions of Linear Dependence and
Independence as a language that does not discard the notions given by Euler,
Frobenius, Grassmann or Peano, but keep them in a unifying and generalizing
character.
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