msm555
Answered

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Prove that the set of all three dimensional vectors forms a group under the operation addition.​

Sagot :

Every vector space is an abelian group under addition. It's an axiom

Proof:-

[tex]V =\{ x = ( x_{1} ,x_{2} ,x_{3}) | x_{i}∈K\}[/tex]

[tex]V\times V→V ,( x_{1} ,x_{2} ,x_{3})+( y_{1} ,y_{2} ,y_{3})=( x_{1} +y_{1},x_{2}+y_{2},x_{3}+y_{3}) [/tex]

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