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.

Quote:

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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)

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Choose, for example, .