Unformatted text preview: f1 . 2. Let V be a ﬁnite dimensional vector space of dimension n . For W ≤ V deﬁne 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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 Winter '07
 Aschbacher
 Math, Linear Algebra, Algebra, Apostol, Mathematics Math 1b

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