Consider the linear mappings F: R³ R³, G: R³ → R2 and H: R2 R³, given by the formulae below. F(x₁, x2, 3) = (4. x₁ +5. X2, X2 + x3, x1 — X3), G(x1, x2, 3) = (4x₁ − 5 x2 + 20 x3, -20 x₁ + 25x2 - 100 x3), H(x1, x2) = (4x₁,-4. x1, x1 + x₂). (A) One of these maps is not injective. Which is it? (No answer given) [3marks] [3marks] (B) One of these maps is not surjective. Which is it? (No answer given) (C) In the case of the non-injective map, what is the dimension of its kernel? (D) In the case of the non-surjective map, what is the dimension of its image? [3marks] [3marks]