Let V be the set of all positive real numbers Determine whether V is a vector space with the given operations. X +Ỹ = XỶ cX = X° if it is verify axioms 4, 8,9.
Let V be the set of all positive real numbers Determine whether V is a vector space with the given operations. X +Ỹ = XỶ cX = X° if it is verify axioms 4, 8,9.
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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![1. the set V is closed under vector addition, that is , x +y E V
2. The set V is closed under scalar multiplication, That is c1·X€ V
3. Vector addition is commutative, that is x + y = y +x
4. vector addition is associative, that is (x +y) + z =x+(y+z)
5. There is a zero vector 0 E V such that x + 0 = x for all x e V
6. For each x there is a unique vetro –x such that x +
-x) = 0
7. (c1 + c2) ·X = c1X+ C2X
8. c1 · (x+ y)= c1 · x + ci ·y
9. (c1c2) · x = c1•)c2·x)
10. 1·x = X](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fed56e0b6-cbbe-4a68-a52e-39451a9af167%2Fbc64c5df-2da3-44c3-962b-7cae5a700d1a%2Fk0tblxm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. the set V is closed under vector addition, that is , x +y E V
2. The set V is closed under scalar multiplication, That is c1·X€ V
3. Vector addition is commutative, that is x + y = y +x
4. vector addition is associative, that is (x +y) + z =x+(y+z)
5. There is a zero vector 0 E V such that x + 0 = x for all x e V
6. For each x there is a unique vetro –x such that x +
-x) = 0
7. (c1 + c2) ·X = c1X+ C2X
8. c1 · (x+ y)= c1 · x + ci ·y
9. (c1c2) · x = c1•)c2·x)
10. 1·x = X
![Let V be the set of all positive real numbers Determine whether V is a vector space with the
given operations.
X +Ỷ = XỶ
cX = X°
if it is verify axioms 4, 8,9.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fed56e0b6-cbbe-4a68-a52e-39451a9af167%2Fbc64c5df-2da3-44c3-962b-7cae5a700d1a%2Fqfvlkkl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let V be the set of all positive real numbers Determine whether V is a vector space with the
given operations.
X +Ỷ = XỶ
cX = X°
if it is verify axioms 4, 8,9.
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