Show all your work in the space provided under each question. Each problem is worth 10 points except for problem 14. which is worth 20 points: find a linear transformation t : r3 r3 which rotates points by an angle of. 4 radians in a counterclockwise direction around the z-axis when viewed from the positive z-axis: draw a picture of the indicated set. Label all vertices on the gure you draw. {su + tv : 1 s 2, 1 t 1} where u = (1, 1), v = (0, 2): consider t : r4 r3 given by t (x) = ax where. Find a basis for the nullspace of t and a basis for the image of t : in m (2, 2) determine if the matrices (cid:20)1 0. 0 linearly independent: find a matrix p so that p 1ap is diagonal where a = (cid:20)1 3. 3 1(cid:21): let s be a set of vectors contained in rn.
