Answer to Question #86511 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) }
Show that
P^(e)={ summation of i (ai *x^i)€ R[x] | ai=0 if i is odd.}
P^(o)={ summation of i (ai *x^i)€ R[x] | ai= 0 if i is even.}
Deduce that P^(o) intersection P^(e) ={0}.

Answer 1

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