4. (a) Determine if the set S = {at² + bt+c: a - 2b = 3c} ⊆ P₂ is a vector subspace of P₂. I (8 marks)
(b) Determine if the set S = {(a, b, c): a ≥ 0} ⊆ R³ is a vector subspace of R³ (6 marks)
(c) Consider the subset K of all invertible nxn matrices and determine if it is a subspace of Mnxn · (6 marks)