Matrices Question

2. [10 marks] Write down the 2 x 2 matrices that represent the following linear trans- formations of the plane. Also draw the image of the (first quadrant) unit square 01 under each transformation. (a) A dilation with horizontal dilation factor 1/2 and vertical dilation factor 2. (b) A vertical shear with factor -1/2. (c) A rotation of 30 anticlockwise. (d) A reflection across the line at angle -30 to the X-axis. (e) The transformation T(x, y) = (2x + 4y, x + 2y)