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# h1 - V is a subspace W 1 = f X ∈ V f(0 = 5 W 2 = f X ∈...

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Homework Set 1 for MAS 4105 The following problems are due on Friday, January 20: 1. Determine whether the set V = R 2 with the indicated operations is a vector space over R . ( x 1 ,x 2 )+( y 1 ,y 2 ) = ( x 1 + y 1 ,x 2 + y 2 ) c ( x 1 ,x 2 ) = ( cx 1 , 0) If V is a vector space over R then verify that all the axioms hold. If V is not a vector space then prove this by showing that one of the axioms does not hold. 2. Let V = P 3 ( R )bethevectorspaceofpolynomialsofdegree 3over R . Determine with proof whether each of the following subsets of
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Unformatted text preview: V is a subspace. W 1 = { f ( X ) ∈ V : f (0) = 5 } W 2 = { f ( X ) ∈ V : f (4) = 0 } W 3 = { f ( X ) ∈ V : f ′ (0) = 0 and f (7) = 0 } W 4 = { f ( X ) ∈ V : f ′ (0) = 0 or f (7) = 0 } The following problems are strongly recommended, but should not be turned in: 1.2: 1, 2, 3, 4aceg, 8, 14, 15, 17, 18 1.3: 1, 2, 3, 4, 5, 6, 8, 11, 15, 17, 18, 20 1.4: 1, 2ace, 3ace, 4ace, 5, 6, 7, 8, 9, 11...
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