Answered: Consider the vector space R^4 and u =…

Consider the vector space R^4 and u = (u1, u2, u3, u4) ∈ R^4 . 1. Let Q : R^4 → R defined by Q(u) = |u3| + |u4| + sup{|u1|, |u2|}. Determine if Q is a norm, a seminorm or none of the two for R^4.

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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Question

Consider the vector space R^4 and u = (u1, u2, u3, u4) ∈ R^4 . 1. Let Q : R^4 → R defined by Q(u) = |u3| + |u4| + sup{|u1|, |u2|}. Determine if Q is a norm, a seminorm or none of the two for R^4.

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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