Let U and W be vector spaces over a field K. Let V be the set of ordered pairs (u,w) where u ∈ U and w ∈ W. Show that V is a vector space over K with

Tazmin Horton 2021-02-25 Answered

Let U and W be vector spaces over a field K. Let V be the set of ordered pairs (u,w) where uU and wW. 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)
(This space V is called the external direct product of U and W.)

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Nathalie Redfern
Answered 2021-02-26 Author has 99 answers
B is a vector space over K with addition in V and scalar multiplication by V
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