Let V be a vector space over F field and $\displaystyle f: V \rightarrow \mathbb{F}$ is nonzero linear functional. So $\displaystyle f(\alpha u+\beta v) = \alpha f(u) + \beta f(v)$ for every $\displaystyle u,v \in V$ and $\displaystyle \alpha , \beta \in \mathbb{F}$. Show that for every $\displaystyle \lambda \in \mathbb{F}$ $\displaystyle H_\lambda =\{ x \in V | f(x) = \lambda \}$ is a hyperplane.

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