This project gives a brief introduction to 2-D computer graphics. Students will learn how collections of points in R can be visualized and how different linear transformations applied to these points manipulate and alter the original shape, Your answers to the problems should be typed into a single Word document. You should show your work for each part of each problem. Figures you create for this assignment can be hand drawn and scanned, or you can sketch them in PowerPoint, Paint, or any other software tool of your choice. Visualizing Linear Transformations of the Plane provides general background theory on this topic and who works similar examples to those you are asked to work below. Problem: 1. Find a 2 x 2 matrix that maps e to er and er to enter 2. Consider the linear transformation described by the matrix A - . . Note that arbitrary points on the x-axis can be written as fo for s e Rand arbitrary points on the y-axis can be written as " for ?'E R. To what set of points does this transformation map the x-axis to? To what set of points does this transformation map the y ads to? 3. Define the unit square as the collection of points in R. with vertices (0,0), [0, 1). (1,0), and (1,1). Sketch the unit square. 4. For each of the following linear transformation matrices, sketch the transformation of the unit square. As - 1 97.42 - 19, 21.4, - [cos (8/4) sin (x/4) cos (w/4) 5. Find a transformation matrix that maps the unit square to the parallelogram with vertices (0,0], (2.41, (1,3), and (3,7)