# 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

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

(This space V is called the external direct product of U and W.)

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Nathalie Redfern
B is a vector space over K with addition in V and scalar multiplication by V