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HINGES - An Illustration of Gauss-Jordan Reduction - Conclusions

Przemyslaw Bogacki

I implemented the HINGES activity in a way that would make it compatible with a variety of systems and browsers. Teaching a class in a distance learning mode, no assumptions can usually be made about "standard" configurations, plug-ins, etc. The trade-off of this approach is that the interactivity available to a student is limited.

I am currently working on more interactive models, where a user can

  • choose a different initial augmented matrix to work with,
  • choose the sequence of "door/wall/ghost" plane selections -- for example, to try various pivoting strategies,
  • rotate and zoom the 3D view (rather than dealing with the fixed view afforded by the pre-generated animations).

The following screen snapshot is taken from a Mathcad-based implementation of such an interactive model. The middle section of the document serves as a control panel: the radio buttons allow for altering the "door/wall/ghost plane" sequence, while the sliders control the rotation of the chosen door plane -- positioning the slider in the middle corresponds to no rotation.

Among the future plans, I am considering creating a JAVA version of the HINGES activity that will provide at least the functionality of the Mathcad model.

I designed this activity for an introductory linear algebra class, without any emphasis on the numerical aspects. However, it may be very appealing to incorporate illustrations of this type when discussing Gaussian elimination pivoting strategies (Poole and Neal, 1991) in a numerical linear algebra course.

Przemyslaw Bogacki, "HINGES - An Illustration of Gauss-Jordan Reduction - Conclusions," Convergence (June 2005)