Question

Determine if the given set is a subspace of P4. Justify your answer. All polynomials of degree at most 4, with integers as coefficients. Complete each statement below. The zero vector of P4 in the set because zero an integer The set v closed under vector addition because the sum of two integers an integer The set closed under multiplication by scalars because the product of a scalar and an integer an integer Is the set a subspace of P4? 0 Yes O No

Answer 1

PETER talee Pa : {eota, 24 92 x't dog x3 +9428/8,0, 19e argiaa EIR} na & aa+a ,kta ,x?tag zetaczek (arca, 0,1% act23 õ=otortox?tox?to se and this belong to because gaan aga=0 and is integer a.NEW i uz autą, at az a 27 aga²fqae Na altal set cup 2+2 3+ a x² where a 3 az, as, a En. atv (bota, ta z²t az et qq x4) + caltalstal 2, cartazh utra cataos +(atadz + carta ² tazas 22 t la tau) 24 since addition of int eger is innegen Gtal a tal on tai azt az auta ez وهوه فيه يمه يمه 7 W is :uty E ka w is closed under addition, closed ander sea lan multiplication since af W and tata? take ka 52 scalar ther kan 52 coefficient not integer Wis not subspace of fe 5 +522+ 52 = 2¢1.