$V,W$ are linear spaces.$ U\_1,U\_2$ are sub-spaces of $V$.

Also given, $\dim U\_1 = \dim U\_2 = 2n$ and there is a linear transformation $T: V \rightarrow W$

also $\dim (U\_1 + U\_2) = 3n$

prove that: $\dim (T(U\_1 \cap U\_2)) \le n$

I started by saying that it's obviously $\dim (U\_1 \cap U\_2) = n$.

but I didn't manage to continue from here.