Is the set of all vectors in $R2$ of the form $(a, b)$ where $b = a$ closed under addition?

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Answer 1 · 2017-04-01T18:45:05

Yes. For Proof , refer to The Explanation.

Let $V={(a,b) : a=b in RR} ={(a,a) : a in RR} sub RR^2.$

Let $vecx=(a,a) and vecy=(b,b)$ be arbitrary vectors of $V, where, a,b in RR.$

By the Defn. of Addition of Vectors,

$vecx+vecy=(a,a)+(b,b)=(a+b,a+b)=(c,c)," say, where, "c=a+b in RR.$

Clearly, $vecx+vecy in V.$

This shows that $V$ is closed under vector addition.

Enjoy Maths.!

Is the set of all vectors in R2R2 of the form (a, b)(a, b) where b = ab = a closed under addition?