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Unformatted text preview: { u 1 ,..., u m } ⊕ span { v 1 ,..., v n } . (c) Suppose u 1 ,..., u m are linearly independent but u 1 ,..., u m , v are linearly dependent. Show that v ∈ span { u 1 ,..., u m } and v can be uniquely expressed as a linear combination of u 1 ,..., u m . 4. Let V be a vector space and u 1 ,..., u n ∈ V . For all i = 1 ,...,n , let W i = span { u 1 ,..., u i } and let W = { } . Show that u 1 ,..., u n are linearly independent if and only if W i1 ( W i for i = 1 ,...,n. Recall that the notation A ( B means two things: A ⊆ B and A 6 = B . Date : February 28, 2008 (Version 1.1); due: March 6, 2008. 1...
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This note was uploaded on 08/01/2008 for the course MATH 110 taught by Professor Gurevitch during the Spring '08 term at University of California, Berkeley.
 Spring '08
 GUREVITCH
 Math, Linear Algebra, Algebra, Vector Space

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