Animated Matrix-Vector Multiplication

 

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Objective:  This quick demo illustrates matrix-vector multiplication Ax, computed as linear combinations of the columns of A.

Level:  This demo is appropriate for any course in linear or matrix algebra.

Prerequisites:  Ideally, students should be familiar with linear combinations of vectors, but the animation could be used to motivate the concept of linear combination.

Platform:  This animation is designed to be run from the Internet using any Java-capable browser.

Instructor's Notes:  The animation illustrates the matrix-vector product, Ax, computed as linear combinations of the columns of A.  The weights in the linear combination are the components of x.  The scalar multiples of the columns are computed, then the sum of the resulting vectors is displayed.  

Each time the java applet is started, a new matrix and vector product is computed.  The speed of the action of the applet can be controlled using the sliders.

To obtain a separate page with the applet, press here.

Credits:  This demo was contributed by Alan Genz, Department of Mathematics, Washington State University and is included in Demos with Positive Impact with his permission.

Other demonstrations/tutorials are located at the URL

http://www.sci.wsu.edu/math/faculty/genz/220v/lessons/tutorials.html

The java applet demonstrated here was developed by C.J. Kentler who was a graduate assistant at WSU.



LFR 5/16/00       Last updated 5/22/2006   DRH

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