Yes, that is correct.

But obviously I'm wrong since S+T is a subspace and what I have is clearly not a subspace. How do you get the 0 vector from S+T?Whydo you conclude that S+ T is a subspace?

Yes, S and T areThanksss.

***Correction - S+T is a subspace only if S and T are both subspaces, and that would explain the zero vector thing... So is my calculation correct?? And does that mean that in this particular example S+T is not a subspace??notsubspaces so S+ T is not necessarily a subspace. And in this case, it isn't.