I. [7 marks] (a) Write down the 2 2 matrices that represent the following linear 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 1 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 poin (0,) to (-1/V2,-1/v2) and (1,0) to (-1/v2,1/V2) 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 T3(x, y)x+ y, Vr y). Is this transformation a mirror reflection? If so, what is the reflection line? (Hint: write this transformation a11 a12 as a matrix product T3 (x,y) --T3( | ) A 721 a22 compare A to the form of a reflection matrix, by guessing an appropriate angle from the drawing.) 4. A degenerate transformation T4 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 D when applying the following transformations to it: Ti, T2, T1 followed by T2, and T2 followed by T1 (c) Compute A1 A2 and A2A1. Do the matrices A and A2 commute and is this in line with the result of part b