Let Uj and U2 be vector subspaces of a vector space V over the real numbers. Suppose that v1, V2, V3 is a basis for U1 and V4, V5, V6 is a basis for U2. Suppose that UinU2 = 0. Prove that B = = V1, V2, V3, V4, V5, V6 is a basis for U1 + U2.

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