Prove that in a real vector space #V# #c(alpha - beta ) = c*alpha - c*beta # where #c in RR ; alpha,beta in V# ?

1 Answer
Narad T.
Oct 2, 2017

See the explanation below

Explanation:

The #2# operations allowed in a vector space are addition and scalar multiplication. They are called the standard operations on #V#

#AA u in V, EE -v in V#, this is called the additive inverse of #u#

Here, we have

#alpha , beta in V# and #c in RR#

Therefore,

#c(alpha-beta)=c(alpha+(-beta))#

Removing the parenthesis

#c(alpha-beta)=c(alpha+(-beta))=c.alpha+c.(-beta)#

#=c.alpha-c.beta#

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