Problem and addition () by s] Let R+ be the set of positive real numbers. Define scalar multiplication (o) ax = xa for all x R+, α = R xy=xy, for all x, y = R+ -4 = 16, and the addition of 3 For example, the scalar product of -4 times ½ is -4 0 1 = (})¯ and 7 is 37=3.7 = 21. 5) Considering the operations and H, is R+ a vector space? Yes No. Justify your answer (briefly explain why each of the axioms A1 to A8 hold or fail) (x = − z = x + (y = z). A1 x y = y = x. A2 A3 x0 =x=0x. A4 xinv(x) = 0. A5 A6 a ○ (x = y) = a ° x = a ○ y. (a+b)ox=aox Box. A7 ao (Box) = (aẞß) ox. A8 10x = x. Commutativity of addition. Associativity of addition Exists a neutral element for add. Every x has an inverse inv(x). Vectors distribute. Scalars distribute. Associativity of scalar multiplication. Scaling by 1 gives the same.

Problem and addition () by s] Let R+ be the set of positive real numbers. Define scalar multiplication (o) ax = xa for all x R+, α = R xy=xy, for all x, y = R+ -4 = 16, and the addition of 3 For example, the scalar product of -4 times ½ is -4 0 1 = (})¯ and 7 is 37=3.7 = 21. 5) Considering the operations and H, is R+ a vector space? Yes No. Justify your answer (briefly explain why each of the axioms A1 to A8 hold or fail) (x = − z = x + (y = z). A1 x y = y = x. A2 A3 x0 =x=0x. A4 xinv(x) = 0. A5 A6 a ○ (x = y) = a ° x = a ○ y. (a+b)ox=aox Box. A7 ao (Box) = (aẞß) ox. A8 10x = x. Commutativity of addition. Associativity of addition Exists a neutral element for add. Every x has an inverse inv(x). Vectors distribute. Scalars distribute. Associativity of scalar multiplication. Scaling by 1 gives the same.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.3: Zeros Of Polynomials

Problem 32E

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