part c pleaseeee Consider the following vector structure.Let the vectors be ordered pairs (a, b) with a, b real numbers and b > 0.So examples of vectors here would be (V8, 2), (-5, ), (0, 7)Define the following operations on these ordered pairs.Note: Let k be any scalar with the scalars for this space being all real numbers.(a, b) O (c, d) = (ad + bc, bd)ko (a, b) = (kabk-1,8*)(a) Calculate (-4, 5) O (3, })(b) Calculate – o (8, 4)(c) Verify all 10 axioms to show that this structure defines a vector space over the real scalarsHints1) Remember the zero vector in a vector space is not necessarily just made of zeroes.2) Remember the zero vector must satisfy: 0 = 0 0 v3) Remember that additive inverses must satisfy,-v = -1 © v

Note: According to bartleby we have to answer only first three proves please upload the rest of the…

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(c) Verify all 10 axioms to show that this structure defines a vector space over the real scalars

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.1: Vector In R^n

Problem 61E: Illustrate properties 110 of Theorem 4.2 for u=(2,1,3,6), v=(1,4,0,1), w=(3,0,2,0), c=5, and d=2....

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Question

part c pleaseeee

Consider the following vector structure.
Let the vectors be ordered pairs (a, b) with a, b real numbers and b > 0.
So examples of vectors here would be (V8, 2), (-5, ), (0, 7)
Define the following operations on these ordered pairs.
Note: Let k be any scalar with the scalars for this space being all real numbers.
(a, b) O (c, d) = (ad + bc, bd)
ko (a, b) = (kabk-1,8*)
(a) Calculate (-4, 5) O (3, })
(b) Calculate – o (8, 4)
(c) Verify all 10 axioms to show that this structure defines a vector space over the real scalars
Hints
1) Remember the zero vector in a vector space is not necessarily just made of zeroes.
2) Remember the zero vector must satisfy: 0 = 0 0 v
3) Remember that additive inverses must satisfy,
-v = -1 © v

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