Answer to Question #86512 in Linear Algebra for RAKESH DEY

Question

Let P^(e)= {p(x)€R[x] | p(x)=p(-x) }
P^(o)={p(x)€R[x] | p(x)=-p(-x) }
Check p(x)+p(-x) € P^(e) for every p(x) € R(x). Check that the map ¥:R[x] tends to P^(e) given by ¥(p(x))= [( p(x)+p(-x))/2] is a linear map. Further, check that¥^2=¥. Determine the kernel of ¥.

Answer 1

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