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H is not a subspace of R.

H is not a subspace of R.

Advanced Engineering Mathematics
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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Please solve 3 and 6

2.8 EXERCISES Exercises 1-4 display sets in R2. Assume the sets include the bounding lines. In each case, give a specific reason why the set H is not a subspace of R?. (For instance, find two vectors in H whose sum is nor in H, or find a vector in H with a scalar multiple that is not in H. Draw a picture.) 1. 2. 3. 5. Let v = and w = Deter- 10 mine if w is in the subspace of R' generated by vị and v2. 6. Let v = and u = Determine if u is in the subspace of R' generated by {v, V, va}
Transcribed Image Text:2.8 EXERCISES Exercises 1-4 display sets in R2. Assume the sets include the bounding lines. In each case, give a specific reason why the set H is not a subspace of R?. (For instance, find two vectors in H whose sum is nor in H, or find a vector in H with a scalar multiple that is not in H. Draw a picture.) 1. 2. 3. 5. Let v = and w = Deter- 10 mine if w is in the subspace of R' generated by vị and v2. 6. Let v = and u = Determine if u is in the subspace of R' generated by {v, V, va}
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