Questions 18-27 are about the matrix exponential et. Write five terms of the infinite series for et. Take the derivative of each term. Show that you have four terms of AeAt. Conclusion: eAt uo solves u' Au. 18 19 20 21 328 22 The matrix B [8] has B = 0. Find et from a (short) infinite series. Check that the derivative of eBt is BeBt. 23 = Starting from u(0) the solution at time 7 is eAT u(0). Go an additional time / to reach eAt eAT u(0). This solution at time + 7 can also be written as Conclusion: eAt times eAT equals Write A = [] in the form SAS-. Find et from Set S-1. Chapter 6. Eigenvalues and Eigenvectors If A = A show that the infinite series produces et = 1+(e-1) A. For A = [] in Problem 21 this gives e eAt = Generally ee is different from eBeA. They are both different from e4+ B Check this using Probleme