questions below:

Find a fundamental matrix for the system x' (t) = Ax(t) for the given matrix A. 710 A: E) Choose the correct answer below. e5t e2t _285t _5e2t O A. X0): 0 B. X\"): _235t _5e2t e5t e2t ezt e5t _232t _5est O c. X0): 0 D. X\"): '282t _5e5t e2t 5t Verify that X(t) is a fundamental matrix for the given system and compute X_ 1 (t). Then use the result that if X(t) is a fundamental matrix for the system x' = Ax, then x(t) = X(t)X_ 1(0)x0 is the solution to the initial value problem x' = Ax, x(0) = x0. o 6 0 -1 24e-t '36_2t Seat x'= 101 x, x(0)= 1 ; X(t)= 4e't e'2t aea' 110 5 202't ezt Seat 0 6 O (a) If X(t) = [x1 (t) x2 (t) x3(t)] and A = 1 O 1 , validate the following identities and write the column vector that equals each side of the equation. 1 1 0 x1 / =Ax1 = x2/ \"\"2 = x3/ \"\"3 = (b) Next, compute the Wronskian of X(t). W [x1 (t),x2 (t),x3 (t)] = Since the Wronskian is never , and each column of X(t) is a solution to x' =Ax, X(t) is a fundamental matrix. (c) Find x' 1m = (d) X(t) = X(OX _ 1 (leo =