Please can you guys help me to solve the following questions
Q1.if Z is an (n-1)-dimensional subspace of an n-dimensional vector space X, show that Z is the null space of suitable linear functional f on X, which is uniquely determined to within a scalar multiple.
note that the linear functional φ in this case is the dual vector to the basis element xn.
note also that since n = dim(X) = null(φ) + rank(φ) = null(φ) + 1, dim(null(φ)) = n-1.
it is a theorem that every hyper-space (or hyper-plane) arises in this fashion.