Given the importance of linear algebra in many engineering and science courses, research has been carried out into the teaching and learning of linear algebra. One of the current research problems is how to integrate digital artefacts into the teaching and learning of linear algebra contents. In order to help solve this problem, we present a case study, carrying out a qualitative descriptive and interpretative investigation, on the use of a Computer Algebra System (CAS) in teaching matrix addition and scalar multiplication establishing instrumental orchestrations and a type of task that provide epistemic practices. We carried out an analysis of teaching practice in the natural classroom environment of a teacher of linear algebra, identifying the instrumental orchestration the teacher used to introduce Octave in teaching matrix addition and scalar multiplication, the changes she did to the way she usually taught these contents without Octave and if it use promoted epistemic practices. We obtained the main characteristics of the instrumental orchestration for the teaching of matrix addition and scalar multiplication using Octave and the ones of the tasks: exploitation task and systematization task.