In Exercises 3-12, determine whether each set equipped with the given operations is a vector space. Forvector spaces identify the vector space axioms that fail.11. The set of all pairs of real numbers of the form (1, x) with the operations(1, y) + (1y')= (1, y +y') and k(1, y) = (1, ky)

Answered: 11. The set of all pairs of real…

11. The set of all pairs of real numbers of the form (1, x) with the operations (1, y) + (1. ")= (1,y +y') and k (1, y) = (1, ky)

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.2: Vector Spaces

Problem 38E: Determine whether the set R2 with the operations (x1,y1)+(x2,y2)=(x1x2,y1y2) and c(x1,y1)=(cx1,cy1)...

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Question

In Exercises 3-12, determine whether each set equipped with the given operations is a vector space. For
vector spaces identify the vector space axioms that fail.
11. The set of all pairs of real numbers of the form (1, x) with the operations
(1, y) + (1y')= (1, y +y') and k(1, y) = (1, ky)

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