This is a tool to calculate the several important quantities and matrices related to another matrix
Type of Material:
A part of in-class demonstration or a tool to accompany a take-home project.
Requires a "Java-enabled" browser.
Identify Major Learning Goals:
To see several important aspects of a matrix that would otherwise be tedious to come up without technology.
Target Student Population:
Linear Algebra Students
Prerequisite Knowledge or Skills:
An understanding of matrices, such as rank, determinant, inverse, etc.
This is part of a larger WIMS site that includes specialized calculators from several areas of mathematics. This learning object calculates the rank, determinant, trace, signature, inverse, powers of a matrix, the characteristic polynomial, the eigenvalues, the eigenvectors, and any polynomial expression in A or the inverse of A. The program can even handle symbolic entries such as x for an entry. The layout is clear and the results are written in an easy-to-read format. In particular the eigenvalues and eigenvectors are displayed in a tabular format with the eigenvalue, multiplicity, and eigenvector as columns.
When there are fractions in the inverse matrix, the numbers overlap, making it difficult to read the actual numbers. When the characteristic polynomial is of degree larger than 2, the calculator cannot handle the computation of eigenvalues and eigenvectors. It just states that the computation failed.
Potential Effectiveness as a Teaching Tool
This calculator quickly produces the quantities related to the matrix. It can be used as a tool to supplement the theoretical parts of linear algebra in a form of in-class demonstrations, as a tool for a take-home project, or as an element of self-guided study. An instructor can talk about the theory and then use this object to show a matrix example. The site has links to Wikipedia explanations of the terms related to matrix theory.
It relies on Wikipedia links only for instruction. An instructor would need to create a worksheet with explanations and exercises in order for students to effectively learn from this tool.
Ease of Use for Both Students and Faculty
The instructions are short and easy to follow. An average user can start using this applet immediately. When a matrix is inputted incorrectly, there is a simple warning message that attempts to explain why the input was incorrect. There is a help button that explains how to use the calculator for the most difficult process: registering a matrix so that more than one matrix can be used at once. Since the computations are mostly queried using check boxes, there is little that can go wrong with the program.
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