# (n-1)-dimensional subspace is the null space of a linear functional

## Main Question or Discussion Point

Given that N is an (n-1)-dimensional subspace of an n-dimensional vector space V, show that N is the null space of a linear functional.

My thoughts:

suppose $$\alpha_i$$($$1\leq i \leq n-1$$) is the basis of N, the linear functional in question has to satisfy f($$\alpha_i$$)=0.

Am I correct?

Thanks

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