3. |40 points + 5 (abc) are the last 3 nonzero digits of your student ID. Let A = SDS- where S= =[ x2] and D= : (a) 5 What is the determinant of S? (b) 10 Find the inverse of S, S-1, using any method. (c) 10 Calculate A, where A = SDS-1. (d) 6 Show Avi = av, and Ave = buz, where S = [v1 82]. (e) 4 Find the solution to the system of differential equations Hint: I strongly suggest using the previous part's (3d) answer. (f) 5 Show for Extra Credit that the substitution S- $ = changes the system in (h) to (g) 2 s = Cul + C212 = 0 always has exactly one solution, namely S- = . Why does this mean the columns of S are linearly independent? (h) 2 s @ = Cul + C212 = |always has a solution, namely , = 5- ] Why does this mean the columns of S span R2? (i) 1 Why do the columns of $ form a basis for IR