Click on the left graph to sketch a polyonal curve.
Type in the entries of the matrix.
Click on animate to watch the image of your polygonal curve
under the powers of the matrix. The computer will sketch A^{n}x
where A is your matrix and x is the coordinates of the vertices of the
polygonal curve. Click the stop button to stop the animation.
Use the step button to watch the image one power at a time.
Click on the clear button to start over with a new curve and
a new matrix.
When you have explored with the applet enough that you feel that
you are comfortable with the dynamics of matrices, try the following written
exercises. Please answer each with a few complete sentences and then back up
each answer with an example.
Written Exercises
What is the effect of a diagonal matrix on the curve.
Answer for positive values, negative values, and values both in absolute
value less than and greater than 1.
What is the effect of the matrix on the curve if the matrix
is triangular with 1's on the diagonal? Please answer this for both
upper and lower triangular matrices.