Use the following steps to prove that if ABBA then eAt+Bt = eAteBt. (a) Show that...
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Use the following steps to prove that if ABBA then eAt+Bt = eAteBt. (a) Show that x(t) = eAt+Bt satisfies the initial-value problem x=(A+B)X, X(0) = I (b) Show that eAB = Bet if AB = BA (hint: A B = BA if AB = conclude that (d/dt)etet = (A+B)eteBt. BA.) Then, Use the following steps to prove that if ABBA then eAt+Bt = eAteBt. (a) Show that x(t) = eAt+Bt satisfies the initial-value problem x=(A+B)X, X(0) = I (b) Show that eAB = Bet if AB = BA (hint: A B = BA if AB = conclude that (d/dt)etet = (A+B)eteBt. BA.) Then,
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