In this work, students' thinking modes and representation types in linear algebra are investigated through statistical implicative analysis techniques. Specifically, our research question considers the implicative relationships between students' thinking modes and representation types of linear algebra. The participants were 74 undergraduate linear algebra students enrolled in the department of mathematics education of a government university located in western Turkey. The data was collected using six paper-and-pencil tasks, relating to a context of linear equations, matrix algebra, linear combination, span, linear independency-dependency and basis. A document analysis technique was used to analyze the data within a theoretical lens of thinking modes and representation types. To delineate similarity diagrams, hierarchical trees, and implicative models (which will be detailed in the paper), an R version of Cohesion Hierarchical Implicative Classification software was used. According to the results, students' analytic structural thinking modes on linear combination and span and linear independency significantly imply the use of algebraic and abstract representations. The results also confirm that the notions of linear combination and span and linear dependency/independency are core elements for theoretical thinking and are needed for learning linear algebra.