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Let U and W be subspaces of V, let u1,...,um be a basis of U, and...

Let U and W be subspaces of V, let u1,...,um be a basis of U, and let w1,....,wn be a basis of W. Show that if u1,...,um,w1,...,wn is a basis of U+W then U+W=U ⊕ W is a direct sum

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