Hi,

I have this problem to solve.

Prove or give a countterexample: If U_1, U_2, U_3 are subspaces of a finite dimensional vector space V, then

dim(U_1+U_2+U_3)=dim(U_1)+dim(U_2)+dim(U_3)-dim(U_1(interset)U_2)-dim(U_2(interset)U_3)-dim(U_3(interset)U_1)+dim(U_1(interset)U_2(interse t)U_3)

Can you help me, please!