Question

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

Vectors and spaces
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asked 2021-02-25

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

Expert Answers (1)

2021-02-26
B is a vector space over K with addition in V and scalar multiplication by V
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