Below are problems we have used in the past for homework. Instructors should feel free to use any subset of these that they feel would be beneficial to their students. 1. Supposethat T:R* R? is defined by T(x) = Ax, where A = [ g] a. Find the images of the following vectors under T: x=[ly=[lw=[T}u=v= b. Sketch the original vectors on one graph and the images of the vectors on a second graph. Do something like the following, where the graph on the left sketches x, y, w, u, and v, and the graph on the graph sketches their images under the transformation. . Describe in words what the transformation defined by A does to the vectors. What does the transformation do to the entire space? How did you reach this conclusion