... 0. Letx(t):=x 1 (t) −x2(t),x 0 := x 1 − x2.25Then˙x(t)=Mx(t), x (0) = x 0 =0, butNx(t) =0 (t ≥ 0) .Nowx(t)=X(t)x 0 = etMx 0 .ThusNetMx 0 =0 (t ≥ 0) .Let t = 0, to find Nx 0 = 0. ... thatp(M) =0. So if we writep(λ)=λn+ βn 1 λn 1 + ···+ β 1 λ 1 + β 0 ,thenp(M)=Mn+ βn 1 Mn 1 + ···+ β 1 M + β 0 I =0. ThereforeMn= −βn 1 Mn 1 − βn−2Mn−2−···−β 1 M − β 0 I,and ... =1, A =[ 1, 1] , and write x(t)=(x 1 (t),x2(t))T. Suppose˙x 1 =0 ˙x2= α(t).This is a system of the form˙x = Mx + Nα, forM = 00 00 ,N= 0 1 Clearly C = {(x 1 ,x2) | x 1 =0} ,...