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5. Let U1, U2, U3 be subspaces of a vector space V. Prove that U1, U2,...

5. Let U1, U2, U3 be subspaces of a vector space V.

Prove that U1, U2, U3 are direct-summable if and only if

(i) the intersection of U1 and U2 is 0.\, and

(ii) the intersection of U1+U2 and U3 is 0.

A detailed explanation would be greatly appreciated :)

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