Question

linear algebra 2 part mcq

H Let be the set of third degree polynomials H = {ax + ax? + ax' | AEC) P3 why or why not? H Is a subspace of Select all correct answer choices (there may be more than one). a. H P3 is a subspace of because it can be written as the span of a subset of b. H is a subspace of because it contains only second degree polynomials ICH Ра is not a subspace of because it is not closed under scalar multiplication d. H is not a subspace of P because it does not contain the zero vector of e. H is not a subspace of Р. because it is not closed under vector addition f. H P3 is a subspace of because it P3 contains the zero vector of & H is a subspace of because it is closed under vector addition and scalar multiplication

part a

part b

Answer 1

(а) +} = {ax tax*+ ах* 1 ас є } = show ! +++*} :. Hiko Sub spa e • Р. fet a2+ar+ax3 and be+bx+623CH. K, Be с. « ( ах+ axtax 3) + B ( bx + bx+3) = lea+Bь) х +la+b)='t wa + Bь)х* (х + 4+2+(x* ең аrе c – «Q+РЬ 6 С. немес. Ні да израве ЕГ, . option (a) and (8) are tone. ка 3 (b) - 3 T А 1 -2 -3 6 4. - 6 а! - 10 9-9 4 - 6 9 - 3 о о- R2 - К: +3 , в, -е, -4, B4-к, +8 Кs - fs - як,

] -2 -3 3 o o 0 6 o 2 -3 0 -8 -9 12 24 -27 0 8 R3 I 2 R3 R4 / R4 - 2 -3 3. 0 o 1 w o -4. 4 0 -1 -3 0 8 24 -27 Rq3 24 th3, RS RS-8R3. - 2 3 o 0 0 0 - 3 o 0 3-4 0 0 - 0 0 o 0 5 R,,,R3 and Rs are 4 3. CIA) = Linearly independent -2 -3 -3 3 4 -4 6 10 CIA) = 2 3 -3 6 foue. option (b) and (d) are