Verify all vector space axioms and determine, if the set of all triples of real numbers (x,y,z) is a vector space under the given operations (x,y,z) + (x',y',z') = (x+x', y+y', z+z') and k(x,y,z) = (0,0,0)

Verify all vector space axioms and determine, if the set of all triples of real numbers (x,y,z) is a vector space under the given operations (x,y,z) + (x',y',z') = (x+x', y+y', z+z') and k(x,y,z) = (0,0,0)

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 24CM

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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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