Mathematics · Convex Sets & Linear Algebra

Given the expressions below: (i) αx + βy where α + β = 1 (ii) αx + βy where α + β > 1 (iii) (1 - α)x + (1 - β)y where 0 < α < 1, 0 < β < 1 (iv) αx + (1 - α)y where 0 ≤ α ≤ 1 Which of the above represent valid convex combinations of x and y?