Dear Colleagues,

Could you please help me in solving the problem:

If $\displaystyle Z$ is an $\displaystyle (n-1)-$dimensional subspace of an $\displaystyle n-$dimensional vector space $\displaystyle X$, show that $\displaystyle Z$ is the null space of a suitable linear functional $\displaystyle f$ on $\displaystyle X$, which is uniquely determined to within a scalar multiple.

Regards,

Raed.