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  3. (10pt) let v and w be a vector space over r. show

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

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Advance Math

  1. (10pt) Let V and W be a vector space over R. Show that V × Wtogether with (v0,w0)+(v1,w1)=(v0 +v1,w0 +w1) for v0,v1 ?V, w0,w1?W

    and

    ?·(v,w)=(?·v,?·w) for ??R, v?V, w?W is a vector space overR.

  2. (5pt)LetV beavectorspaceoverR,?,??R,andu,v?V. Provethat(?+?)(u+v) = ((?u+?v)+?u)+?v.

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

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