QUESTION: In the attached solution for 3b, how do you determine the shear matrix?

3 b) Rotation R about Origin Since Rotation is go degrees in clockwise direction, the rotation matrix IS O Dilation D From the figures, the object , has been multi- Plied by a scaler whose value. D = 2 shear s Since the (shear is to be-axis, shear matrix Is 4 O3. In the diagram below, the 2x2 shaded square centered at the origin is bounded by the lines x = +1 and y = +1. Let T denote the linear transformation that maps the square on the left to the parallelogram at the right. T (a) Use the structure theorem for linear transformations to find the matrix of T. Check your work with a suitable point, e.g. x = [1, 1], (b) Now write T'as a product of three transformations, first a dilation D, second a horizontal shear S, and third a rotation R about the origin. Find matrices for each of the three transformations, and check that their product RSD gives you the matrix of T