Planes, Solutions, and Gaussian Elimination of a 3×3 Linear System

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Gaussian elimination is often used as a pen-and-paper exercise for solving simple linear systems, but the geometric counterpart may remain elusive during this exercise. Use this Demonstration to visualize the planes and solutions of a system of three linear equations as you apply elementary row operations to the system. Alternatively, simply play around with the parameters to visualize various types of solutions.

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Solutions are shown in red, either as a point, a line, or a plane.

The color of each linear equation is repeated by the parameter sliders, the plane, and the normal vector.

Use the tooltips of the user interface as guides.

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Contributed by: Klaus Michelsen (March 2011)
Open content licensed under CC BY-NC-SA


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