Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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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 unde…
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
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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.
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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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