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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 := a bb a R 2 2 a,b R , V 2 := c d dc R 2 2 c,d R . 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...
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 Spring '08
 GUREVITCH
 Math, Linear Algebra, Algebra, Scalar, Vector Space

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