Graphical Demonstration of Linear Transformations on $\mathbb{R}^2$

Question

I'm looking for some applet, program, software, demonstration etc. to use it in a class while teaching linear transformation in $\mathbb{R}^2$, so that the students can graphically understand the effect of different linear transformations on the plane. I've found one as shown in the picture below:

As you can see, we can transform the standard basis for $\mathbb{R}^2$ and see what happens to the purple polygon. I would be much happier if instead of a polygon, we could work with a picture and see the effect of the linear transformation on it. Do you know any such applet or program?

The students in the class are not familiar with the matrices and their product. As a matter of fact, this demonstration is intended to help them grasp the notion of matrix as a linear transformation, later in the course.

Thanks.

Answer 1

I have an applet at http://www.math.cornell.edu/~bterrell/la It is free but is very simple and does not handle pictures. The source code is also on my website so you can improve it if you are so inclined.