Reset the applet by reloading the webpage. The "standard basis" and "arbitrary vector" checkboxes should be ticked. The matrix A and the green vector ~v should be set to: A = [3 1 0 2 ] and ~v = [2 1 ] . (a) Evaluate the product A~v and confirm that it agrees with the vector T (~v) shown in the applet. (b) Notice that ~v = 2~e1 + ~e2, where ~e1 and ~e2 are the standard basis vectors. Since T is linear, it should therefore also be true that T (~v) = 2T (~e1) + T (~e2). Write down the vectors T (~v), T (~e1), and T (~e2), and show that they really do satisfy this relation. Before continuing, tick the "Gauss portrait" checkbox to display a portrait of the German mathematician Carl Friedrich Gauss. Click the tip of the vector ~v and drag it onto one of Gauss's eyes. (You can zoom in by scrolling if the image is too small.) Notice that the transformed vector T (~v) points to the same eye in the transformed portrait on the right. Indeed, this is how the transformed portrait is created. Each point in the portrait is interpreted as a vector in standard position, and when T is applied to that vector, the output vector indicates where that part of the portrait will be located in the transformed figure. 2. To help you answer the two parts of this question, try typing new values into the entries of A and observe how they affect the portrait of Gauss and the standard basis vectors. If you tick the checkbox that says "drag T(e1) and T(e2)," then you can instead drag the tips of T (~e1) an