3. Write the following three dx d matrices 0 1 --:2)-639--03 = LN = 0 0 0 Consider the following linear ODE systems for :'(t) = Jx(t) on (0,0), 2(0) = (1,1,1) € R. (a) Given that 10 -6:9) ---6: :) --:--6:9 100 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 and 0 0 0 0 0 0 0 for a > 3, show by the series definition of exp(EN) that lit exp(N) = 0 1 0 0 2 t 1 (b) Show that DN = ND (c) Given that if AB = BA, the following equality shall always hold: exp(A + B) = exp(A) exp(B), show that eta exp(t) = 0 0 (Hint: Apply the equality to tJ = D+N.) (d) Hence, or otherwse, show that - tett 12 2 eld tell ed 0 z(1)/||2(0)|| ? (1,0,0,...,0) - as t