Let U and W be subspaces of a vector space V such that V = U+W {0} if and only if every vector in V Prove that Un W = can be written uniquely as a linear combination of a vector in U and a vector in W

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A: Solution is given below

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A: See the attachment

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A: here we can use linear combination to prove that given set is linearly independent.

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A: We shall answer first question only as you’ve asked more than one question. For others kindly post…