Question: (25) Let f : D - R, be a bounded function, where D = [a, b] is a closed, bounded interval in R and let

(25) Let f : D - R, be a bounded function, where D = [a, b] is a closed, bounded interval in R and let IIflloo = sup If(t) | tED be the supremum of [f| over D, let F(t) = (fi(t), .., f,(t)) be a vector valued function with f; bounded and let IIF = max |filloo 1 X . Bonus question no marks. Show that X is a complete metric space. . (5) Let L (y ) ( t ) = y(n) ( t) + Pn-1(t ) y (2-1) (t) + ...+ po(t)y(t) where p; (t), 1

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