(10pt) Let V and W be a vector space over R. Show that V × W...

(10pt) Let V and W be a vector space over R. Show that V × W together with (v0,w0)+(v1,w1)=(v0 +v1,w0 +w1) for v0,v1 ∈V, w0,w1 ∈W

and

λ·(v,w)=(λ·v,λ·w) for λ∈R, v∈V, w∈W is a vector space over R.
(5pt)LetV beavectorspaceoverR,λ,μ∈R,andu,v∈V. Provethat (λ+μ)(u+v) = ((λu+λv)+μu)+μv.

(In your proof, carefully refer which axioms of a vector space you use for every equality. Use brackets and refer to Axiom 2 if and when you change them.)

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Expert Solution

Colby Messinger answered 10 months ago

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