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

1 Answer
Apr 1, 2017

Yes. For Proof , refer to The Explanation.

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.!