7 marks] (a) Write down the 2 x 2 matrices that represent t lowing transformations of the plane. Specify for each transformation which points the points (1,0) and (0,1) map to. Also make reasonably accurate drawings (by hand or using MATLAB) of the image of the (first quadrant) unit square under each transformation. You may use the MATLAB program given in Example 6.3 of the Unit Notes to create or check your drawings, which you can copy from the file lintran.m (available on the LMS). Also answer the questions. 1. The transformation Ti that maps point (0,1) to(-1/v2,-1/V2) and (1,0) to (-1/2,1/2) Decide if this transformation is a reflection or a rotation? Provide the relevant angle that describes the transformation. 2. A vertical shear T2 with factor 1 3. The transformation Ts given by Ts(x,y) (3x+v. ^r y). Is this transformation a mirror reflection? If so, what is the reflection line? (Hint: write this transformation 11 12 421 22 as a matrix product Ts(x,y) Ts( compare A to the form of a reflection matrix, by guessing an appropriate angle from the drawing.) 4. A degenerate transformation Ts that maps (1,0) to itself and all points x,y to the y- axis. (you have some choice here for the specific parameters) Verify by calculating the determinant that your transformation is degenerate. (b) Create four diagrams that show the geometric transformation of the unit square when applying the following transformations to t: Ti, T2, T followed by T2, and T2 followed by TI (c) Compute Aj A2 and A2Ai. Do the matrices A and A2 commute and is this in line with the result of part b