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**raed** Dear Colleagues,

Could you please help me in solving the following problem:

If $\displaystyle Y$ is a subspace of a vector space $\displaystyle X$ and codim$\displaystyle Y=1$, then every element of $\displaystyle X/Y$ is called a *hyperplane parallel to* $\displaystyle Y$. Show that for any linear functional $\displaystyle f\neq 0$ on $\displaystyle X$, the set $\displaystyle H_{1}=\{x\in X|f(x)=1\}$ is a hyperplane parallel to the null space $\displaystyle N(f)$ of $\displaystyle f$.

Regards,

Raed.