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Back to Gauss’s Method

Exercise 16

Avg difficulty 3.0

In the system

ax+by=cdx+ey=f\begin{array}{rcrcr}ax&+&by&=&c\\ dx&+&ey&=&f\end{array}

each of the equations describes a line in the xyxy-plane. By geometrical reasoning, show that there are three possibilities: there is a unique solution, there is no solution, and there are infinitely many solutions.

Hefferon, Linear Algebra, Linear Systems, Gauss’s Method, Exercise 16

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Adapted from Linear Algebra © 2016 Jim Hefferon. Licensed under CC BY-SA 3.0 US. Source: Linear Algebra. Imported at revision df2262e.