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Question Number 93505 by Ar Brandon last updated on 13/May/20

Does  (x,y)+(x^′ ,y^′ )=(x+x^′ , y+y^′ )  form a vector space?  λ(x,y)=(λx,λy)

$$\mathrm{Does} \\ $$$$\left(\mathrm{x},\mathrm{y}\right)+\left(\mathrm{x}^{'} ,\mathrm{y}^{'} \right)=\left(\mathrm{x}+\mathrm{x}^{'} ,\:\mathrm{y}+\mathrm{y}^{'} \right) \\ $$$$\mathrm{form}\:\mathrm{a}\:\mathrm{vector}\:\mathrm{space}? \\ $$$$\lambda\left(\mathrm{x},\mathrm{y}\right)=\left(\lambda\mathrm{x},\lambda\mathrm{y}\right) \\ $$

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