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Unformatted text preview: f1 . 2. Let V be a nite dimensional vector space of dimension n . For W V dene the codimension of W in V to be codim( W ) = dim( V )dim( W ). Let W i , 1 i r , be subspaces of V and S = T r i =1 W i . Prove (1) codim( S ) r i =1 codim( W i ). (2) If r i =1 codim( W i ) < n then S 6 = 0. (Hint: Prove (1) by induction on r . In the case r = 2, use the Intersection/Sum Dimension Theorem from recitation section.) 3. Problem 28 on page 43 of Apostol. 1...
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This note was uploaded on 03/03/2011 for the course MATH 1B taught by Professor Aschbacher during the Winter '07 term at Caltech.
 Winter '07
 Aschbacher
 Math, Linear Algebra, Algebra

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