Recall E from the last homework, let = = {[1]:tER} W₁ and W₂ = {[2-1 ]: 1ER} {[²t=1]: 2}. Is W₁ a subspace of R2? If it is, verify this, if not, explain why not. (ii) Is W₂ a subspace of R2? If it is, verify this, if not, explain why not. (iii) Is W₁ a subspace of E? If it is, verify this, if not, explain why not. (iv) Is W₂ a subspace of E? If it is, verify this, if not, explain why not.
Recall E from the last homework, let = = {[1]:tER} W₁ and W₂ = {[2-1 ]: 1ER} {[²t=1]: 2}. Is W₁ a subspace of R2? If it is, verify this, if not, explain why not. (ii) Is W₂ a subspace of R2? If it is, verify this, if not, explain why not. (iii) Is W₁ a subspace of E? If it is, verify this, if not, explain why not. (iv) Is W₂ a subspace of E? If it is, verify this, if not, explain why not.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Recall E from the last homework, let
=
= {[1]:tER}
W₁
and
W₂ = {[2-1 ]: 1ER}
{[²t=1]: 2}.
Is W₁ a subspace of R2? If it is, verify this, if not, explain why not.
(ii) Is W₂ a subspace of R2? If it is, verify this, if not, explain why not.
(iii) Is W₁ a subspace of E? If it is, verify this, if not, explain why not.
(iv) Is W₂ a subspace of E? If it is, verify this, if not, explain why not.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4217e83c-b4b2-47da-9d7a-2d6031448fca%2Fd368820d-6c7f-473c-9312-fcf99c714b0b%2Fpexm11p_processed.png&w=3840&q=75)
Transcribed Image Text:Recall E from the last homework, let
=
= {[1]:tER}
W₁
and
W₂ = {[2-1 ]: 1ER}
{[²t=1]: 2}.
Is W₁ a subspace of R2? If it is, verify this, if not, explain why not.
(ii) Is W₂ a subspace of R2? If it is, verify this, if not, explain why not.
(iii) Is W₁ a subspace of E? If it is, verify this, if not, explain why not.
(iv) Is W₂ a subspace of E? If it is, verify this, if not, explain why not.
Transcribed Image Text:Equip R2 with addition , and scalar multiplication, © by
(:) - ()-(*+*+1)
a
and
cx+c-1
** (*)-(~+21)
=
cy+c-1
Verify that these definitions of addition and scalar multiplication turn R² into a vector space.
We will call this vector space E.
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