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Question Number 185694 by Spillover last updated on 25/Jan/23

Show that the set V=R^3  with  standard vector addition and  multiplication defined as  c(u_1 ,u_2 ,u_3 )=(0,0,cu_3 )

$${Show}\:{that}\:{the}\:{set}\:{V}=\mathbb{R}^{\mathrm{3}} \:{with} \\ $$$${standard}\:{vector}\:{addition}\:{and} \\ $$$${multiplication}\:{defined}\:{as} \\ $$$${c}\left({u}_{\mathrm{1}} ,{u}_{\mathrm{2}} ,{u}_{\mathrm{3}} \right)=\left(\mathrm{0},\mathrm{0},{cu}_{\mathrm{3}} \right) \\ $$

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