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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.
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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
not sure if that was supposed to be p(t)=... but the same argument would apply
\[p(t)-a+t^2+q(t)-(-a)+t^2=p(t)+q(t)+2t^2=p(t)+q(t)+2t^2+a-t^2-a+t^2\] \[=h(t)-a+t^2\]
....Whoops, that was a typo. But thank you! I think I understand it a little better now.
oh
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well I was totally wrong then listen to Zarkon, as usual
unless it was p=
apply what TT did to \[p(t)=-a+t^2\] and you will get your answer
Yeah, it was p=. My bad, but thanks!
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