1. Consider the vector space R2×3 and the subset b0] - {[6 8]₁4 | a,b=R}. H Show that H is a subspace of R²×3. -a
1. Consider the vector space R2×3 and the subset b0] - {[6 8]₁4 | a,b=R}. H Show that H is a subspace of R²×3. -a
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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Need help with this matrix algebra question
![1.
Consider the vector space R²×3 and the subset
b
= { [ 2 ] LabER}
a‚b≤R}.
a,
-a b
H
Show that H is a subspace of R²×3
2.
Let H = {A € R³×3 | A is not invertible}. Show that H is not a subspace of
the vector space R³×3. Note that it suffices to give one concrete example that violates
one of the properties of a subspace.
3.
Consider the vector space P3 of polynomial functions of degree at most 3.
Let H = {ao+a₁t+ a₂t² + 1³ | ao, a₁, a2 € R}. Show that H is not a subspace of P3.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F517e5bdb-4058-44ef-80d0-20aa8be73e5b%2Fb8a42d41-252c-482e-8d83-93db33a7cf23%2Fvzv4rcp_processed.png&w=3840&q=75)
Transcribed Image Text:1.
Consider the vector space R²×3 and the subset
b
= { [ 2 ] LabER}
a‚b≤R}.
a,
-a b
H
Show that H is a subspace of R²×3
2.
Let H = {A € R³×3 | A is not invertible}. Show that H is not a subspace of
the vector space R³×3. Note that it suffices to give one concrete example that violates
one of the properties of a subspace.
3.
Consider the vector space P3 of polynomial functions of degree at most 3.
Let H = {ao+a₁t+ a₂t² + 1³ | ao, a₁, a2 € R}. Show that H is not a subspace of P3.
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