Problem 3. Determine whether the following polynomials are linearly independent in the vector space P of polynomials: (i) 2, x², x and 2x + 3; (ii) x + 2, x + 1 and 2² - 1.

3: Which of the following sets are closed under scalar multiplication? (1) The set of all vectors in R of the form (a, b, 9ab). (i1) The set of all polynomials a- bx+ cx in P, such that ac =D0. (iii) The set of all matrices in Mn such that A = A (A) (1) and (ii) only (B) (1) and (iii) only (C) (ii) and (iii) only (D) (1) only (E) (ii) only (F) none of them (G) (iii) only (H) all of them

1. Determine whether the following polynomials span P. =1+x, p, = 1 – x, P2 P3D1+x+x², P, = 2-x² 3D2 3:28 PM 豆 IA 2/23/2022 e Type here to search WQHD | 165HZ NOG ZEPHYRUS 100% DC-P3 PANTONE Validated F1 F2 F3 F4 F5 F6 F7 F8 F9 F10 F11 F12 ESC E3 O/京 DELETE AURA 23 24 4 @ % & 7 { } TAB Q W E T Y P. [ 1O 15 林

Please answer A, B, and C in question #1.