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Unformatted text preview: c u = then u = or c = 0. 4. Let H be a nonempty subset of vector space V with the following properties: (a) If u , v ∈ H , then 4 u – 5 v ∈ H . (b) If u ∈ H , then c u ∈ H for all scalars c ∈ R . Is H a subspace of V ? 5. Let H,K be subspaces of a vector space V . (a) Is H ∩ K ( H intersection K ) a subspace of V ? (b) Is H ∪ K ( H union K ) a subspace of V ? (c) Is A = { w =u + 2 v : u ∈ H, v ∈ K } a subspace of V ? 1 6 (a) Let V be a vector space. Let v , u ∈ V . Show that span { v , u } is a subspace of V . (b) Let H = s + 4 t st 2 s 3 t : s,t, ∈ R . Is H a subspace of R 4 ? (c) Let V 1 = span 1 2 3 , 1 4 and V 2 = span 82 15 . Is V 2 a subspace of V 1 ? 2...
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 Spring '08
 All
 Math, Scalar, Vector Space, Complex number

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