Unformatted text preview: 2 for the direct sum of three or more subspaces. (b) Let W 1 ,W 2 ,W 3 be subspaces of a vector space V . Suppose W 1 ∩ W 2 = W 1 ∩ W 3 = W 2 ∩ W 3 = { } . Must W 1 + W 2 + W 3 be a direct sum? 5. Prove or provide a counter example for the following. (a) Let V 1 := ±² a bb a ³ ∈ R 2 × 2 ´ ´ ´ ´ a,b ∈ R µ , V 2 := ±² c d dc ³ ∈ R 2 × 2 ´ ´ ´ ´ c,d ∈ R µ . Is it true that R 2 × 2 = V 1 ⊕ V 2 ? (b) Let W 1 := { p ( x ) ∈ P 3  p (x ) = p ( x ) for all x ∈ R } , W 2 := { p ( x ) ∈ P 3  p (x ) =p ( x ) for all x ∈ R } . Is it true that P 3 = W 1 ⊕ W 2 ? Date : February 14, 2008 (Version 1.0); due: February 21, 2008. 1...
View
Full Document
 Spring '08
 GUREVITCH
 Math, Linear Algebra, Algebra, Addition, Scalar, Vector Space, w1 w2

Click to edit the document details