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Mathematics-Online course: Preparatory Course Mathematics - Linear Algebra and Geometry - Systems of Linear Equations

Linear System of Equations with three Variables

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A linear sytem of equations in three variables $ x_1$, $ x_2$, $ x_3$ has the form

a_{11}x_1 &+& a_{12}x_2 &+& a_{13}x_3...
a_{31}x_1 &+& a_{32}x_2 &+& a_{33}x_3 &=& f_3 \,.

The set of all solutions of such a system can be geometrically interpreted as the intersection of the three planes given by the system's equations. The following situations may occur: Such a linear system can be solved by elimination of variables or by Gaussian transformation with subsequent back substitution, for instance.
(Authors: Wipper/Abele)

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  automatically generated 1/9/2017