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Unformatted text preview: MATH 223 PROBLEM SET 3 DUE: 18 SEPTEMBER 2007 When you hand in this problem set, please indicate on the top of the front page how much time it took you to complete. Reading. 2.42.6. Problems from the book: the starred problems will be graded. 2.4.2, 2.4.4, 2.4.5, 2.4.6 , 2.4.12 . 2.5.2 , 2.5.3, 2.5.8 , 2.5.9, 2.5.12, 2.5.15, 2.5.18. Additional problems: 1. Prove one of the following statements. (a) If ( v 1 , . . ., v n ) spans V , then so does the list ( v 1 v 2 , v 2 v 3 , . . ., v n 1 v n , v n ) obtained by subtracting from each vector (except the last) the following vector. (b) If ( v 1 , . . ., v n ) is linearly independent in V , then so is the list ( v 1 v 2 , v 2 v 3 , . . ., v n 1 v n , v n ) obtained by subtracting from each vector (except the last) the following vector. (c) Suppose that ( v 1 , . . .v n ) is linearly independent in V , and w V . If the list ( v 1 + w, . . ., v n + w ) is linearly dependent, then w span ( v 1 , . . ., v, ....
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 Fall '07
 HOLM

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