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determine if the set U is a subspace of the vector V by showing the 3 properties or explaining why it's not.

determine if the set U is a subspace of the vector V by showing the 3 properties or explaining why it's not.

V= vector space of all differentiable functions with domain R
U= the subset of V such that U={g/g'=g+1}

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If f and g ∈ U then we have f = f + 1 and g = g + 1 so consider af + bg
(af + bg ) = af + bg
= a(f + 1) + b(f + 1)
= af + bg + a + b = af + bg + 1
Hence af + bg ∈ U hence U is not a vector...

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