3. (5 points) Compute the rank and nullity of each given matrix and verify Theorem 4.19 in Section 4.9. (Note: This means you cannot apply the theorem, you need to compute the rank and nullity from the matrix and check that it matches the theorem). 1 2 2 a. (2 points) A = 01 2 34 1 102 03 319 0 7 b. (3 points) B= 128 10 217 1 5 4. (5 points) (Section 4.8, Problem 25) Let S = (V1, V2), and T where = (W1, W2) be ordered bases for P, Wt, W2=t1. If the transition matrix from S to T is 2 1 determine S (i.e. find v and V2). Show all work.