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-

Tinku Tara June 4, 2023 Algebra 0 Comments

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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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-

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