Hints:

: A subspace of a vector space is called a hyperplane iff it is a maximalS\Definition

subspace of it, i.e.

Claim: a subspace of a vec. sp. is a hyperplane iff it is the kernel of a non-zero linear

functional on the space

Claim: a subspace of a finite dimensional v.s. is a hyperplane iff its dimension is one less

that then space's.

Tonio