Annihilator of a vector space

[rawkerrxx]

If W1 and W2 are subspaces of V, which is finite-dimensional, describe A(W1+W2) in terms of A(W1) and A(W2). Describe A(W1 intersect W2) in terms of A(W1) and A(W2).

A(W) is the annihilator of W (W a subspace of vector space V). A(W)={f in dual space of V such that f(w)=0 for all w in W}.

 

[daon]

Its been awhile since I've studied linear algebra, but what do you mean by the addition of two subspaces? What does W1+W2 mean? Union?

The second one seems easy enough: if F is in both A(W1) and A(W2) then it annihilates all vectors w belonging to W1 and W2, but more importantly their intersection. So F must be contained in A(W1 intersect W2). So [A(W1) intersect A(W2)] is a subset of A(W1 intersect W2). I'm not sure if that's the answer you're looking for.

 

[rawkerrxx]

Oh I see that. What about the reverse inclusion? I'm being told that A(W1+W2) is contained in A(W1) intersect A(W2) as well, but I don't understand how to prove that.