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| Reviewed: |
Dec 01, 2004 by Mathematics |
| Overview: |
This applet allows the user to visually go through the Gaussian elimination
algorithm for the solutions of systems of equations and the inversion of
matrices. The size of the coefficient matrix can be chosen from 2?2 to 10?10 and
the underlying ring or field of numbers can also be chosen.
Row operations are either input through an instruction field or automatically by
clicking on a coefficient that is to be eliminated or reduced to 1.
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| Learning Goals: |
Gaussian elimination. In an abstract algebra class, comparison of the ways in
which different number fields work is another possible use.
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| Target Student Population: |
Students in college algebra, linear or abstract algebra.
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| Prerequisite Knowledge or Skills: |
Linear systems of equations. For the advanced version of the applet the
knowledge of algebraic structures is required
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| Type of Material: |
Simulation
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| Recommended Uses: |
Classroom demonstration as well as self study.
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| Technical Requirements: |
Should run in any browser.
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| Strengths: |
The standard operations in Gaussian elimination are implemented correctly and
conveniently. The automatic elimination of coefficients is very nice and the
description of the operation assures that the user is updated on what happened
mathematically.
The number of operations necessary for completion is counted and the score is
given once the exercise is completed.
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| Concerns: |
none
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Potential Effectiveness as a Teaching Tool |
Rating:   |
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| Strengths: |
The applet can run in two modes: as a system of linear equations and as a
matrix. This gives an opportunity to use this tool in college algebra and in
linear algebra classes.
In an abstract algebra course this applet can be used to illustrate Gaussian
elimination in modulo arithmetic fields.
As a classroom demonstration with the automatic elimination disabled, this tool
allows a quick demonstration of the solution, even of larger systems of
equations, without the danger of computational mistakes. For self-study and
self-testing, students could do the same thing, or they could predict how the
automatic elimination eliminates a coefficient.
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| Concerns: |
It could be useful to allow the user to input a system of equations or matrices.
Then again, this would lead many students to the temptation of using the site
as an automatic homework solver, so the current implementation may well be the
best.
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Ease of Use for Both Students and Faculty |
| Rating: |
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| Strengths: |
Very easy to use in either input mode.
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| Concerns: |
There is some danger that the automatic elimination of coefficients could lead
to ?blind clicking?. Then again, no technology is immune to inappropriate uses.
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| Other Issues and Comments: |
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