Give an example of linear subspaces U 1 , U 2 , U 3 {\displaystyle {}U_{1},U_{2},U_{3}} in a vector space V {\displaystyle {}V} such that V = U 1 + U 2 + U 3 {\displaystyle {}V=U_{1}+U_{2}+U_{3}} , such that U i ∩ U j = 0 {\displaystyle {}U_{i}\cap U_{j}=0} for i ≠ j {\displaystyle {}i\neq j} holds, and such that the sum is not direct.
