# Math Help - vector subspaces

1. ## 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.

2. ## Re: vector subspaces

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