A Computational Approach to Systems of Linear Equations

  • Franz PauerEmail author
Part of the ICME-13 Monographs book series (ICME13Mo)


We present a purely algebraic/computational approach to systems of linear equations. It requires only a little previous knowledge. We define a system of linear equations as a task, discuss how to specify the input and output data and elucidate the basic ideas to solve the system. Geometric interpretations of systems of linear equations (for the case of two or three unknowns) are postponed to the last section. Firstly, because precise geometric reasoning is not simple but quite demanding, secondly, most applications need systems of linear equations with more than three variables.


System of linear equations Elementary transformation Echelon form Gaussian elimination Implicit form of a line 


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  2. Meyer, C. (2000). Matrix Analysis and Applied Linear Algebra. Philadelphia: SIAM.Google Scholar
  3. Pauer, F. (2007). Lineare Algebra 1. Lecture notes (in german). Innsbruck: University of Innsbruck. (9th edition 2016).

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Institut für MathematikUniversity of InnsbruckInnsbruckAustria
  2. 2.Institut für FachdidaktikUniversity of InnsbruckInnsbruckAustria

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