Let $V=U \bigoplus W$, $V \approx U \times W$. Note that $U,W$, are finite dimensional subspaces of the vector space V, and also that $U \bigoplus W$ means $V=U+W$ and $U \cap W = \{0\}$
I'm really not sure how to go about this, because it doesn't seem to be true to me. But after some research, it does seem to be true. Thanks in advance.