# Dimensions of sum and intersection of vector subspaces

$L_1$ and $L_2$ are vector subspaces of the vector space $V$ with finite dimension.

Prove: If $\dim(L_1+L_2) = 1 + \dim(L_1\cap L_2)$ than the sum $L_1+L_2$ equals to one of the subspaces and the intersection $L_1\cap L_2$ equals the other one.

I can see why it's true, and I've tried to use the dimension theorem but couldn't evaluate it.

Any ideas?

Hint: ($L_1\cap L_2)\subset L_i \subset (L_1 + L_2)$. What if you apply $\dim(\cdot)$?