Unformatted text preview: conjugate) 3. (a) Let V be the real vector space R R and let V even , V odd be the subsets of V consisting the even and the odd functions respectively. Show that V even , V odd are subspaces of V and that V = V even ⊕ V odd . (b) Using (a), give the decomposition of the function f ( x ) = e x into its even and odd component functions. 4. If V is a vector space, prove or disprove the following statements: (a) The intersection of any family of subspaces ( W i ) i ∈ I of V is a subspace of V . (b) If U 1 ,U 2 ,W are subspaces of V with U 1 ⊕ W = U 2 ⊕ W then U 1 = U 2 ....
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 Winter '06
 TOTH
 Algebra, Vector Space, x1 + x2, Vodd

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