Which of the following are subspaces of R°?
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.CM: Cumulative Review
Problem 23CM
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Step 1
PART - A-
Concept Used:
is said to be subspace of the vector space V if
Given:
We want to check is it subspace of
Solution:
Let be any vectors in Then from (1) we get
Now
we need to show that
Now
Therefore
Also for any scalar k to show that that is so
We have to show that
But
Thus
Therefore both conditions are satisfied
Hence is subspace of
Step 2
PART - B-
Concept Used:
is said to be subspace of the vector space V if
Given:
We want to check is it subspace of
Solution:
Let be any vectors in Then from (1) we get
Now consider
Therefore
Therefore first conditions are not satisfied
Hence is not subspace of
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