Let V be a subspace of ℝn with dim(V) = n − 1. (Such a subspace is called a hyperplane in ℝn.) Prove that there is a nonzero x ∈ ℝn such that V = {v ∈ ℝn |x ・ v = 0}. (Hint: Set up a homogeneous system of equations whose coefficient matrix has a basis for V as its rows. Then notice that this (n − 1) × n system has at least one nontrivial solution, say x.)