This site contains a Java applet that allows a user to solve a system of three linear equations with three variables. The applet also calculates the determinant of a coefficient matrix.
Type of Material:
In-class demonstration or a part of self-guided study.
Requires a "Java-enabled" browser.
Identify Major Learning Goals:
To provide a simple and effective tool for solving systems of linear equations.
Target Student Population:
Linear Algebra Students
Prerequisite Knowledge or Skills:
A basic course in elementary Linear Algebra.
Evaluation and Observation
The applet is straight-forward and intuitive: the user types entries into the 3 by 4 matrix representing the system of three linear equations with 3 unknowns, then clicks on a Solve It button. The solution then appears below the system, with entries computed to 6-digit precision. The applet also computes the determinant of a coefficient matrix of the system. The reviewers found no errors in the results. When the determinant is zero, the computer gives the message of either Null or Dependent depending on whether there is no solution or an infinite number of solutions.
The layout is clear and the results are written in an easy to read format.
While simplicity can be a virtue, in this case it results in an unfortunate limitation of the applets usefulness. There is no provision for the user to adjust the size of the system, so that systems with different number of equations/variables cannot be handled at all.
Also when a user is trying to use a fraction (not in the decimal format) as one of the coefficients, the applet refuses to run.
Potential Effectiveness as a Teaching Tool
The applet efficiently carries out a computation which would be hard to do by hand. As mentioned above, it could lend itself to experimentation and conjecture on number of solutions and consistency of a linear system with three equations and three variables.
The applet can be used as an aid to a lecture or as a quick in-class demonstration.
The site would benefit from adding an introductory paragraph or a link to a site containing relevant theoretical material on the subject. Since this is a tool only, an instructor would have to provide both the lesson plan and the background information to the student.
Ease of Use for Both Students and Faculty
The applet has only one button found and is very easy to use. The average user can begin using the applet immediately. When the user omits a coefficient or types in a non-numeric character, the object gives a message of Fix Inputs.