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Let L and T be two linear functionals on a real vector space $V$ such that $L(v) = 0$ implies $T (v) = 0$. Show that $T = cL$ for some real number $c$.

how can i prove the above problem. clearly converse part is true.but how can i proceed in this case.

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    @did: How is a linear functional supposed to be invertible unless $V$ is one-dimensional?2012-11-02
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    @wj32 Right. Sorry about the noise.2012-11-03
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    Consider this approach. Given $N(L) \subset N(T)\,,$ where $N$ is the null space of the linear functional. Assume $v\in N(L)\,,$ then we have $$ T(v)=L(v)=0=L(cv)=cL(v) \implies Tv-cLv=0 \implies (T-cL)(v)=0 \implies T=cL \,. $$2013-01-06

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