# Three questions on the annihilator

(a) Prove that if $ U ⊂ V$ is a linear subspace then $U^\circ $ is also a linear subspace of $V^*$.

(b) If $f \in V^*$ is a non-zero element how is $(Span(f))^o $ related to $ker f$?

(c) When $V = R^3$, describe the subspace $(Span(\epsilon^2 + \epsilon^3))^\circ$.

More info on the annihilator is found in the image.

I think for question (b) you need to show that $\Psi(ker(f))=(Span(f))^\circ$ (and you possibly need the Lemma in the image as well).

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