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Three Views of Systems of Linear Equations - Editorial Review

Dan Kalman

This Mathwright Microworld consists of three pages coinciding with the "three views" alluded to in the title: Simultaneous linear equations, vector equations, and matrix/vector equations. The first of these pages uses the standard "intersection of lines" model for systems of two equations and two unknowns -- the user clicks points on the screen to test them for satisfiability of the two equations, and a graph of either or both lines can then be produced to check the correct answer. The second "view" has the user visually (by dragging the heads of vectors to scale them) finding the appropriate linear combination of two given vectors to produce a given resultant vector. The third page uses a user-defined 2 by 2 matrix A to represent the system of equations, and the user chooses (by mouse drag) "domain vectors" until one is found whose image (under the transformation A) matches the given resultant vector. In all three cases, a discussion of the model is given before the related activity, and sample exercises for exploration are given immediately thereafter. Note that this module is based on Mathwright Microworld technology. To use it, one must first download and install the MathwrightWeb ActiveX Control (which is available for free) for Internet Explorer. There is also a stand-alone (Windows only) version available on the site.

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Dan Kalman, "Three Views of Systems of Linear Equations - Editorial Review," Convergence (June 2004)