Question: midterm question Problem 1.Let T: Ri[r] - Rar] be the linear transformation given by the formula T(p(x)) = / p(x)dx, where you find the antiderivative

midterm question

Problem 1.Let T: Ri[r] - Rar] be the linear transformation given by the formula T(p(x)) = / p(x)dx, where you find the antiderivative of p(r) (take the integration constant as zero). (a) Find the matrix [T] - relative to the bases B = 2r + 1,2x - 1] and B' = [1,1,x]]. (b) Find the kernel of T. (c) Decide whether 7 is injective and surjective. (d) Verify the dimension theorem given in lecture (Week 10, 27.04)

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