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Solving methods of systems of linear equations
Šotolová, Petra ; Jančařík, Antonín (advisor) ; Novotná, Jarmila (referee)
My bachelor's thesis is focused on methods for solving systems of linear equations. Its aim is to explain the application of these methods for solving systems of linear equations and to assign advantages and the type of system for which each method is advantageous. The thesis should be suitable for elementary and secondary school students, university students, as well as individuals not studying mathematics. It describes substitution method, addition method, comparison method, graphical method, Gaussian elimination, Gauss-Jordan elimination, inverse matrix and Cramer's rule and their application in solving systems of two or more linear equations with two or more unknowns. It includes a general explanation and a specific procedure with examples, advantages and disadvantages of each method, and types of systems for which the method would be used. The thesis examines the number of solutions of systems of equations depending on the form of the system. It also explains basic concepts and provides simplified definitions of the terms used.
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Application for graphical solution of linear programming problems
Nebesová, Anna ; Sekničková, Jana (advisor) ; Kuncová, Martina (referee)
Linear programming problems with maximally three variables can be solved graphicaly. The aim of this thesis is to create an application in Microsoft Excel using VBA that graphicaly solves any linear programming problem with two variables, compute the optimal solution and display feasible solution set. At first, finding a graphical solution by hand is explained. Further, the code of the application and the application itself is described. The thesis also includes a list of problems occurred in the process and their solution if found. Finally, possible extensions are suggested and the user manual including errors and bugs is written.
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