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# 1) Determine if the set U is a subspace of the vector space V. If yes show the 3 properties, if no explain why.

1) Determine if the set U is a subspace of the vector space V. If yes show the 3 properties, if no explain why...
Let V be the vector space of all continuously differentiable functions on the real line. U is the subset of V such that U={f:f'=3f}

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If f and g ∈ U then we have f = 3f and g = 3g so consider af + bg
(af + bg ) = af + bg
= a × 3f + b × 3g
= 3(af + bg )
Hence af + bg ∈ U hence U is vector subspace of V . 1

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