t.BA.XXM3.LA1.19HS (Linear Algebra 1) 
Module: Linear Algebra 1
This information was generated on: 30 July 2021
Linear Algebra 1
Organised by


Version: 3.0 start 01 August 2019

Short description

Students are familiarised with and master the basic concepts and propositions of linear algebra and analytic geometry. They can formulate simple concrete questions in the mathematical language and are able to solve these independently and present their solutions.

Module coordinator

Landry Chantal (lany)

Learning objectives (competencies)

Objectives Competences Taxonomy levels
You know vectors in two- and three-dimensional space and are familiar with the arithmetic operations of vector geometry. F, M K2, K3
You can analytically describe and solve geometric problems of the plane and the space with the help of the vector calculation. F, M K2, K3
You are familiar with the matrix calculus and can use it. F, M K2, K3
You can formulate linear systems of equations and determine, if these systems are solvable. F, M K2, K3
You know algorithms for solving linear systems of equations and can apply them. F, M K3
You master the essential properties and calculation rules of the determinants. F, M K2
You know algorithms for calculating determinants and can apply them. F. M K3

Module contents

Vector geometry:
  • Definition of free and bound vectors
  • Vector calculus in two- and three-dimensional space
  • Applications in analytic geometry (lines and planes)
  • Definition of a real Matrix and special square matrices
  • Arithmetic operations on matrices
  • Invertible matrix
System of linear equations:
  • Definition of a linear system and its representation using matrices
  • Solvability of a linear system and rank of a matrix
  • Solving a linear system: Gaussian elimination, Gauss-Jordan elimination, Cramer's rule
  • Applications: matrix inversion and evaluating linear independence of a set of vectors
  • Definition of the determinant of a square matrix
  • Properties and calculation rules of the determinant
  • Laplace expansion for computing determinants
  • Applications

Teaching materials

Lecture notes, blackboard sketches, handout

Supplementary literature

Ruhrländer, M.: Lineare Algebra für Naturwissenschaftler und Ingenieure, Pearson Studium
Papula, L.: Mathematik für Ingenieure und Naturwissenschaftler (Bände I und II), Vieweg+Teubner, 12. Auflage
Gramlich, G.M.: Lineare Algebra: Eine Einführung, Carl Hanser Verlag


Knowledge of mathematics of the technical Berufsmatura

Teaching language

(X) German ( ) English

Part of International Profile

( ) Yes (X) No

Module structure

Type 2b
  For more details please click on this link: T_CL_Modulauspraegungen_SM2025


Description Type Form Scope Grade Weighting
Graded assignments during teaching semester at least two assessments written Per assessment max. 45 minutes Grade
count only with a positive 
contribution to the final 
module grade with a total 
of 30%
End-of-semester exam exam written 90 min Grade Min. 70%



Legal basis

The module description is part of the legal basis in addition to the general academic regulations. It is binding. During the first week of the semester a written and communicated supplement can specify the module description in more detail.


Course: Lineare Algebra 1 - Vorlesung
Lineare Algebra 1 - Vorlesung


  • No module description is available in the system for the cut-off date of 01 August 2099.