24.  Let W1 and W2 be subspaces of a finite-dimensional vector space V. Let ⊕ denote the direct sum. Which of the following statements are correct?


(A) W1 ∩W2 is a subspace of V.


(B) W1 ∩W2 is a subspace of V.


(C) W1+W2 is a subspace of V.


(D) If V = W1 ⊕W2, and β1 and B2 are bases for W1 and W2, respectively, then β1 and B2 = 0, and β1 ∪ β2 is a basis for V. 


(E) If  W1 ⊕ W2 = V, then the dimension dim(V) = dim(W1)+dim(W2).

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