Which of the following sets are closed under scalar multipli

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Which of the following sets are closed under scalar multiplication?
(i) The set of all vectors in R2 of the form (a, b) where a + 4b = 4
.(ii) The set of all 2 × 2 matrices whose trace is equal to 1.
(iii) The set of all polynomials in P2 of the form a0 + a1 x + a2 x2 where the product a0 a1 a2 ≤ 0.
(A) (i) only (B) (iii) only (C) (i) and (ii) only (D) (i) and (iii) only (E) none of them (F) (ii) and (iii) only (G) all of them (H) (ii) only
Which of the following sets are closed under addition?
(i) The set of all vectors in R2 of the form (a, b) where b = a2.
(ii) The set of all 3 × 3 matrices that have the vector [-2 3 2]T as an eigenvector.
(iii) The set of all polynomials in P2 of the form a0 + a1 x + a2 x2 where a0 = a2.
(A) (ii) only (B) (i) and (ii) only (C) (ii) and (iii) only (D) (i) and (iii) only (E) (i) only (F) (iii) only (G) all of them (H) none of them

选C 因为这个矩阵式放行矩阵所以选c

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