Answered: 1. (i) Give the definition of a norm on…

1. (i) Give the definition of a norm on a vector space X. [5 Marks] (ii) Explain why the function ||x|| = |x1 + x2| does not define a norm on the vector space R². [15 Marks]

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.2: Vector Spaces

Problem 40E: ProofProve in full detail that M2,2, with the standard operations, is a vector space.

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Question

1. (i) Give the definition of a norm on a vector space X.
[5 Marks]
(ii) Explain why the function ||x|| = |x1 + x2| does not define a norm on
the vector space R².
[15 Marks]

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