Fixed Point Problem: Figure 11-4d shows a rectangle that is to be the pre-image for a

Chapter 11, Problem 3

(choose chapter or problem)

Fixed Point Problem: Figure 11-4d shows a rectangle that is to be the pre-image for a set of linear transformations. In this problem you will find out which matrix determines the fixed point, the transformation matrix or the pre-image matrix. Figure 11-4d a. Describe the transformations accomplished by matrix [T1]. b. Write a matrix [M1] for the rectangle in Figure 11-4d. Apply transformation [T1] iteratively to [M1] using your grapher program. To what fixed point do the images converge? Show this fixed point on a copy of Figure 11-4d, along with the path the images follow to reach this point. c. Apply transformation [T1] iteratively to another rectangle, [M2] below. Are the images attracted to the same fixed point as for [M1]? Sketch the pre-image and the path the images follow. d. Write a transformation matrix [T2] that performs this set of transformations. A 70% reduction; that is a dilation by a A 35 counterclockwise rotation A translation of 7 units in the x-direction and 3 units in the y-direction Apply [T2] iteratively to the rectangle [M1]. Are the images attracted to the same fixed point as for [T1]? On a copy of Figure 11-4d, sketch the path the images follow to reach the fixed point. e. Based on your results for parts bd, which determines the location of the fixed point attractor, the transformation matrix or the pre-image matrix? Does applying [T2] to [M2] support your conclusion?