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Suppose that $W,W_1$ and $W_2$ are subspaces of a vector space $V$ such that $V=W_1\oplus W_2$. Under what conditions we have $W=(W\cap W_1)\oplus(W\cap W_2)$ ?

this was the firs problem of our exam. does anyone know what is the answer to this problem?

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    Could you clarify please? Are you asking under what conditions on $W$ do we have $W = (W \cap W_1) \oplus (W \cap W_2)$?2012-02-17
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    I wrote exactly the question's statement. I don't know what condition was in mind of our teacher.2012-02-17

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