Determine if the given set is a subspace of Pn for an appropriate value of n. Justify your answer.

All polynomials of the form p(t) - a + t^2, where a is in R.

Question

Determine if the given set is a subspace of Pn for an appropriate value of n. Justify your answer.

All polynomials of the form p(t) - a + t^2, where a is in R.

turingtest · Answer

not closed under addition: a1=a and a2=-a we get$$p(t)-a+t^2+q(t)-(-a)+t^2=p(t)+q(t)+2t^2$$which is not in the form defined

turingtest · Answer

not sure if that was supposed to be p(t)=...
but the same argument would apply

zarkon · Answer

$$p(t)-a+t^2+q(t)-(-a)+t^2=p(t)+q(t)+2t^2=p(t)+q(t)+2t^2+a-t^2-a+t^2$$

$$=h(t)-a+t^2$$

xkehaulanix · Answer

....Whoops, that was a typo. But thank you! I think I understand it a little better now.

turingtest · Answer

oh

turingtest · Answer

well I was totally wrong then
listen to Zarkon, as usual

turingtest · Answer

unless it was p=

zarkon · Answer

apply what TT did to $$p(t)=-a+t^2$$ and you will get your answer

xkehaulanix · Answer

Yeah, it was p=. My bad, but thanks!