Dear Colleagues,

Could you please help me in the following problem:

Let $\displaystyle Z$ be a proper subspace of an $\displaystyle n-$dimensional vector space $\displaystyle X$, and let $\displaystyle x_{0}\in X-Z$. Show that there is a linear functional $\displaystyle f$ on $\displaystyle X$ such that $\displaystyle f(x_{0})=1$ and $\displaystyle f(x)=0$ for all $\displaystyle x\in Z$.

Regards,

Raed.