# [SOLVED] How can U + W be S-invariant even if U and W aren't?

I don't understand how if U and W are subspaces of V such that $S\left ( \vec{u} \right ) \epsilon W,\forall \vec{u}\epsilon U$ and $S\left ( \vec{w} \right ) \epsilon U,\forall \vec{w}\epsilon W$ then U + W will be S-invariant even if U and W aren't. Can someone explain this to me? I need to understand this to make an operator S for 2x2 matrices.
Well if $u+w \in U+W$, then $S(u+w)=S(u)+S(w) \in W+U = U+W$.