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
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