Question

Let    be the set of third degree polynomials

Is    a subspace of   ? Why or why not?

Select all correct answer choices (there may be more than one).

	a.	is not a subspace of    because it is not closed under vector addition
	b.	is a subspace of    because it contains the zero vector of
	c.	is not a subspace of    because it is not closed under scalar multiplication
	d.	is a subspace of    because it contains only second degree polynomials
	e.	is a subspace of    because it can be written as the span of a subset of
	f.	is a subspace of    because it is closed under vector addition and scalar multiplication
	g.	is not a subspace of    because it does not contain the zero vector of

Let H be the set of third degree polynomials H = {ax + ax2 + ax? | a EC} Is H a subspace of P3? Why or why not? Select all correct answer choices (there may be more than one). a. H is not a subspace of P3 because it is not closed under vector addition b. H is a subspace of P3 because it contains the zero vector of P3 c. H is not a subspace of P3 because it is not closed under scalar multiplication d. H is a subspace of P3 because it contains only second degree polynomials e. H is a subspace of P3 because it can be written as the span of a subset of P3 f. H is a subspace of P3 because it is closed under vector addition and scalar multiplication H is not a subspace of P3 because it does not contain the zero vector of P3

Answer 1

→ Here, Hi { av t ad ay an? apel Now ley has apkot a purta pas, where ） aze op, ond, ha anat arust an3 1 where, azec where high EH. thery hyothy = (astanut (ay + 2) u fal tas) 3, } autą te Son of two Complex Complex plumber. member is also a How less CEC. they elhas e Carmen dennot apmale) (ca) & & ka) na leagu? EH, for C, apfc. His closed under addition and sealar moltiplice from subspace. as , can te any thers Hds