Question

4. [10 pts] Define T: P2 → Max2 by T(p)=Ip(0) p(-1) 10(1) p(2) (a) Show that T is a linear transformation. (b) What is the kernel of T? (e) Describe the range of T as the set of 2 x 2 matrices with the entries a,b.c,d satisfying certain conditions. Hint: Work on the practice problem §4.231 first. For finding the kernel, you may use the fact that if a polynomial p has degree at most 3 and p(0) = p(-1) = p(1) = p(2) = 0, then p is the zero polymomial. For finding the range, you may use the fact that if a polynomial p has degree at most 2 then p(-1)-37(0) + 37(1)-p(2-0. d 0with the entries a, b, c, d

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