1. the set V is closed under vector addition, that is , x +y E V2. The set V is closed under scalar multiplication, That is c1·X€ V3. Vector addition is commutative, that is x + y = y +x4. 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 V6. For each x there is a unique vetro –x such that x +-x) = 07. (c1 + c2) ·X = c1X+ C2X8. c1 · (x+ y)= c1 · x + ci ·y9. (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 thegiven operations.X +Ỷ = XỶcX = X°if it is verify axioms 4, 8,9.

Answered: Image /qna-images/answer/bc64c5df-2da3-44c3-962b-7cae5a700d1a.jpg

Answered: Let V be the set of all positive real…

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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Concept explainers

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

Question

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.

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