Answered: Let S be the set of all ordered pairs…

Let S be the set of all ordered pairs of real numbers (x1, x2) equipped with the following operations (x1, x2) ⊕ (y1, y2) = (x1 + y1, 0) α(x1, x2) = (αx1, αx2). Show that S is not a vector space

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CM: Cumulative Review

Problem 5CM: Take this test to review the material in Chapters 4 and 5. After you are finished, check your work...

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Question

Let S be the set of all ordered pairs of real numbers (x1, x2) equipped with the following operations

(x1, x2) ⊕ (y1, y2) = (x1 + y1, 0)
α(x1, x2) = (αx1, αx2).

Show that S is not a vector space.

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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