Mathematics · Linear Algebra

Let us define a matrix A ∈ M n (ℝ) to be positive if for every column vector v ∈ ℝ n we have ⟨Av, v⟩ ≥ 0, where ⟨·,·⟩ is the standard inner product on ℝ n . Let A α, β = α 1 1 1 0 0 1 0 β . Let S = {(α, β) ∈ ℝ 2 : A α, β is positive}. Which of the following statements is true?