16. Let X be an n x p matrix of rank p. Partition X such that X = [X₁, X₂], where X₁ has size n x p₁ and X₂ has size n x p₂ where p₁ + p₂ = p. Show that the rank of B is p₂ where B is defined by B = X(X'X)⁻¹X' - X₁(X₁'X₁)⁻¹X₁'.