In which of the following examples is the set U not a subspace of the space V? (a) V=R2×2, U = {A EV | sled A = 0}.(b) V=R³, U = {(x, y, z) = V | 2x+y-z = 0}.(c) V = R₂[x], U = {p € V | p(0) = 2}.(d) V=R2, U= {(a, b) EV | a=2b}.(e) V C², U={(y, z) = V | y=2z}.

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Answered: =1 (a) V=R2x2, U = {AEV | sled A = 0}.…

=1 (a) V=R2x2, U = {AEV | sled A = 0}. (b) V=R³, U= {(x, y, z) = V | 2x+y-z = 0}. (c) VR₂[x], U = {pЄ V | p(0) = 2}. (d) V=R2, U = {(a,b) € V | a = 2b}. (e) V=C², U= {(y, z) Є V | y=2z}.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.3: Lines

Problem 22E

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Question

In which of the following examples is the set U not a subspace of the space V?

(a) V=R2×2, U = {A EV | sled A = 0}.
(b) V=R³, U = {(x, y, z) = V | 2x+y-z = 0}.
(c) V = R₂[x], U = {p € V | p(0) = 2}.
(d) V=R2, U= {(a, b) EV | a=2b}.
(e) V C², U={(y, z) = V | y=2z}.

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