4. Let U and W be vector spaces over a field K. Let V be the set of ordered pairs (u, w) where u EU and we W. Show that V is a vector space over K with addition in V and scalar multiplication on V defined by (u, w) + (u', w')= (u+u', w+w') and k(u, w) = (ku, kw).

4. Let U and W be vector spaces over a field K. Let V be the set of ordered pairs (u, w) where u EU and we W. Show that V is a vector space over K with addition in V and scalar multiplication on V defined by (u, w) + (u', w')= (u+u', w+w') and k(u, w) = (ku, kw).

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

4. Let U and W be vector spaces over a field K. Let V be the
set of ordered pairs (u, w) where u EU and we W. Show that V is a vector
space over K with addition in V and scalar multiplication on V defined by
(u, w) + (u', w')= (u+u', w+w') and k(u, w) = (ku, kw).

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