Unformatted text preview: A , and consider the map L A : B → [ A,B ] Show that L A is a linear map. Describe the kernel of L A . (3) Let V be the space of inﬁnitely diﬀerentaible functions on the interval [0 , 1]. Show that the map T : V → V deﬁned by ( Tf )( x ) = Z x f ( t ) dt is a linear map. Prove that T is injective. Is T surjective? (Why or whiy not?) 1...
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 Spring '08
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 Math, Linear Algebra, Derivative, Vector Space, Linear map, infinitely differentiable functions

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