To construct each IVP, choose a pair of scalars X and (if complex, and 2 must be complex conjugate) an invertible matrix Uthat is not the identity matrix an initial value xo. If X and are real, set P=U | 2]U-. If = a + iand A = a - Bifor some real numbers a and B, set 0 P=U [ -2]U-. Solve the IVP x' = Px and x(0) = x two different ways: i. Apply the "IKEA method" described in Friday's lecture, using the information that you already know because you used it to construct P. ii. Apply the relevant method described in Notes on Diffy Q's to find the general solution, then solve for the constants C and c to find the solution of the IVP. Verify that you obtain the same answer from both approaches. Problems Create and solve four IVPs, following the instructions given above, one for each of the following situations: 1. Distinct real nonzero and 2 2. = 0 + A 3. A = Biand A = - Bi for real B 4. A = a + iand A = a - Bifor nonzero real numbers a and B,