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…
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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 3, 5,6,7.
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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 3, 5,6,7.
10 Axioms 1. the set V is closed under vector addition, that is , x +y € V 2. The set V is closed under scalar multiplication, That is c1 · x E 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 € V 6. For each x there is a unique vetro -x such that x+ (-x) = 0 7. (С1 + c2) : х — Сіх + с2х 8. c1 · (x+ y) = c1 · x + c1•y 9. (c1c2) · x = cı•)c2 · x) 10. 1: х —Х
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Transcribed Image Text:10 Axioms 1. the set V is closed under vector addition, that is , x +y € V 2. The set V is closed under scalar multiplication, That is c1 · x E 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 € V 6. For each x there is a unique vetro -x such that x+ (-x) = 0 7. (С1 + c2) : х — Сіх + с2х 8. c1 · (x+ y) = c1 · x + c1•y 9. (c1c2) · x = cı•)c2 · x) 10. 1: х —Х
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