This preview shows page 1. Sign up to view the full content.
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 ....
View
Full
Document
This homework help was uploaded on 04/18/2008 for the course MATH 236 taught by Professor Toth during the Winter '06 term at McGill.
 Winter '06
 TOTH
 Algebra, Vector Space

Click to edit the document details