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 R² or give a counterexample to show that it does not. 1. x = 0 2. x2 0, y 2 0 3. y = 2x 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
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 R² or give a counterexample to show that it does not. 1. x = 0 2. x2 0, y 2 0 3. y = 2x 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
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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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 R² or give a counterexample to show
that it does not.
1. x = 0
2. x2 0, y 2 0
3. y = 2x
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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