# vector subspaces

• Oct 17th 2012, 06:35 AM
cassius2020
vector subspaces
I have a vector space A, with B and C are the two subspaces of A.

I need to disprove that dim(B+C)=dim(B)+dim(C)

I know the correct formula should be dim(B+C)=dim(B)+dim(C) - dim(B intersect C)

need to find a counterexample, but am struggling.
• Oct 17th 2012, 07:53 AM
FernandoRevilla
Re: vector subspaces
Quote:

Originally Posted by cassius2020
I have a vector space A, with B and C are the two subspaces of A. I need to disprove that dim(B+C)=dim(B)+dim(C)

Choose, for example, $A=B=C=\mathbb{R}^2$.