[10 marks] In preparation for this question, please watch and work through the four online lec- tures entitled 'Matrices and Linear Transformations (Online lectures)' which are available on LMS/Echo360. (a) Write down the 2 x 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 , 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. A horizontal shear T, with shear factor -1. 2. The transformation 2 that maps point (0, 1) to (1/ v2, -1/ v2) and (1, 0) to (-1/ V/2, -1/ V/2). Is this transformation a simple reflection or a simple rotation? 3. The transformation T3 given by T3(x, y) = (5x + by, -5x By). Is this transforma- tion a mirror reflection? If so, what is the reflection line? (b) Create four diagrams that show the geometric transformation of the unit square , when applying the following transformations to it: T1, T2, T, followed by T2, and T2 followed by T1. (c) Compute Al A2 and A2Aj. Do the matrices Aj and A2 commute and is this in line with the result of part b