In Exercises 1-4, let S be the collection of vectors in R? that satisfy the given property. In each case, either prove that S forms a subspace of R? or give a counterexample to show that it does not. 1. x = 0 2. x 2 0, y z 0 3. y = 2x 4. xy 2 0
In Exercises 1-4, let S be the collection of vectors in R? that satisfy the given property. In each case, either prove that S forms a subspace of R? or give a counterexample to show that it does not. 1. x = 0 2. x 2 0, y z 0 3. y = 2x 4. xy 2 0
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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Only need help with #4 & #6
![In Exercises 1-4, let S be the collection of vectors
in R?
that satisfy the given property. In each case, either prove that
S forms a subspace of R? or give a counterexample to show
that it does not.
1. x = 0
3. у %3D 2х
2. х > 0, у20
4. ху 2 0
In Exercises 5-8, let S be the collection of vectors y in R'
that satisfy the given property. In each case, either prove that
S forms a subspace of R' or give a counterexample to show
that it does not.
5. x = y = z
6. z = 2x, y = 0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Feb88a591-bb84-4ad5-a9d9-9dd6e5ab413a%2Fda73c364-1d7c-4010-a9e8-88e850ac9373%2Fvhngnp_processed.png&w=3840&q=75)
Transcribed Image Text:In Exercises 1-4, let S be the collection of vectors
in R?
that satisfy the given property. In each case, either prove that
S forms a subspace of R? or give a counterexample to show
that it does not.
1. x = 0
3. у %3D 2х
2. х > 0, у20
4. ху 2 0
In Exercises 5-8, let S be the collection of vectors y in R'
that satisfy the given property. In each case, either prove that
S forms a subspace of R' or give a counterexample to show
that it does not.
5. x = y = z
6. z = 2x, y = 0
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