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.
Gaussian elimination. In an abstract algebra class, comparison of the ways in which different number fields work is another possible use.
Target Student Population:
Students in college algebra, linear or abstract algebra.
Prerequisite Knowledge or Skills:
Linear systems of equations. For the advanced version of the applet the knowledge of algebraic structures is required
Type of Material:
Classroom demonstration as well as self study.
Should run in any browser.
Evaluation and Observation
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.
Potential Effectiveness as a Teaching Tool
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.
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.
Ease of Use for Both Students and Faculty
Very easy to use in either input mode.
There is some danger that the automatic elimination of coefficients could lead to ?blind clicking?. Then again, no technology is immune to inappropriate uses.