Answered: Prove that the set of all matrices,…

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Prove that the set of all matrices, under the usual operations is NOT ALWAYS a vector space. Provide a case/example.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CR: Review Exercises

Problem 47CR: Find an orthonormal basis for the subspace of Euclidean 3 space below. W={(x1,x2,x3):x1+x2+x3=0}

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Question

Prove that the set of all matrices, under the usual operations is NOT ALWAYS a vector space. Provide a case/example.

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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