Solved: (Calculus required) Define as follows:For be the

Chapter 4, Problem 34E

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(Calculus required) Define as follows:For be the antiderivative F of f such that F(0) = 0. Show that T is a linear transformation, and describe the kernel of T. (See the notation in Exercise 20 of Section 4.1.)Reference:The set of all continuous real-valued functions defined on a closed interval [a, b] in is denoted by C.[a, b]. This set is a subspace of the vector space of all real-valued functions defined on [a, b].a. What facts about continuous functions should be proved in order to demonstrate that C.[a, b] is indeed a subspace as claimed? (These facts are usually discussed in a calculus class.)b. Show that {f in C [a, b] : f (a) = f (b)} is a subspace of C.[a, b]