problems-3-223-F07

# problems-3-223-F07 - MATH 223 PROBLEM SET 3 DUE 18...

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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. § 2.4–2.6. 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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problems-3-223-F07 - MATH 223 PROBLEM SET 3 DUE 18...

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