> It's painful to read. Problem 2: "Find the matrix A describing the following linear transformation from R2 to R'2 : First rotate clockwise by π/6, then scale

> It's painful to read. Problem 2: "Find the matrix A describing the following linear transformation from R2 to R'2 : First rotate clockwise by π/6, then scale by a factor of 2, then reflect about the x2 axis." Anyone who programs video games recognizes that as a stack of transformations. You set up the matrix for the rotate, the scale, and the reflection (which is a scale of -1 on one axis). You multiply the matrices to get the result. This is a pain to do with pencil and paper. GPUs have hardware for it. > Books on graphics programming cover this problem. But they usually do it much better, with graphical examples. With all due respect to your impressive graphics programming experience, I think even you would have something to learn from this class in general and this problem specifically. The columns of a matrix are where the basis vectors of the domain are mapped. As such, this problem can be done by keeping track of what these operations due to the vectors e_1 and e_2. In particular, it is easy to this problem in your head, never multiplying any matrices along the way.