5. (10 points) Let V be the vector space of all polynomials with coefficients in R....

Transcribed Image Text:

5. (10 points) Let V be the vector space of all polynomials with coefficients in R. We define a map g: V V via the differentiation operation. I.e. for v in V we let g(v) = example f(2x3+7x+1)=(2x +7x + 1) = 6x +7. (a) Show that the map g is a linear map. (b) Is g injective? Explain your answer. (c) Is g surjective? Explain your answer. (v). For 5. (10 points) Let V be the vector space of all polynomials with coefficients in R. We define a map g: V V via the differentiation operation. I.e. for v in V we let g(v) = example f(2x3+7x+1)=(2x +7x + 1) = 6x +7. (a) Show that the map g is a linear map. (b) Is g injective? Explain your answer. (c) Is g surjective? Explain your answer. (v). For