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( * * * The solution for this question must be typed using Latex * * * ) Consider R + = { x :

$(* * $ The solution for this question must be typed using Latex $ * *)$ Consider R $+ = {$ x : x $> 0} .$ We define the following operations:

xy $=$ xy cx $=$ xc forc in R Show that V $= ($ R $+,,)$ is an R $-$ vector space.

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Question

( * * * The solution for this question must be typed using Latex * * * ) Consider R + = { x :

(***The solution for this question must be typed using Latex***) Consider R+={x : x >0}. We define the following operations: xy=xy cx=xc forc in R Show that V =(R+,,) is an R-vector space.

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$(* * $ The solution for this question must be typed using Latex $ * *)$ Consider R $+ = {$ x : x $> 0} .$ We define the following operations:

xy $=$ xy cx $=$ xc forc in R Show that V $= ($ R $+,,)$ is an R $-$ vector space.