Let A = " −1 1 1 −1 # . (a) Find the eigenvalues and eigenvectors, and the exponential e At . (b) Compute d dt(e At) by differentiating each component and confirm that d dt(e At) = AeAt . (c) Solve the system of the differential equations du1(t) dt = −u1(t) + u2(t), du2(t) dt = u1(t) − u2(t), with the initial condition u1(0) = 2, u2(0) = 5.