Visualizing Gaussian Elimination...
Daniel F. Symancyk
Anne Arundel Community College
In this note we will use Maple to demonstrate the geometry associated with the elementary row operations when working with linear systems of two or three variables. We will also give some examples which point out the limitations of technology.
I've recently added two commands, glinsys and geSlideshow, to math191 which is my collection of custom Maple commands. The first command, glinsys, is used to graph the system of equations associated with an n by 3 or n by 4 matrix. When we do this after using a row operation, we can see the effect of the row operation. Once we've completed a problem we can use geSlideShow to get an animation which provides a visual summary of the process.
(Click here to see the contents of the Maple library math191.)Systems in two variables
Three variables (unique solution)
Three variables (no solution)
Three variables (infinite number of solutions)
Where did the plane go?
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