253Homework5

Linear Algebra with Applications (3rd Edition)

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ma253 ,Fa l l 2007 — Problem Set 5 This problem set deals mostly with subspaces, spans, linear dependence and independence, and bases. As usual, solve all the problems, then write up and turn in those marked with an asterisk. Given Fall Break, this assignment is due on Friday, October 26 . 1. Problems from the textbook: a. Section 3 . 1 , problems * 18 ,* 22 ,* 38 ,* 48 . b. Section 3 . 2 , problems 1 ,* 2 , 3 ,* 4 ,* 6 , 8 , 10 , 12 ,* 14 ,* 16 ,* 20 ,* 32 , * 34 ,* 36 ,* 37 . c. Section 4 . 1 , problems 1 ,* 2 , 3 ,* 4 , 5 ,* 12 , 13 , 14 . *2. Suppose you have a linearly dependent set { ~ v 1 , ~ v 2 ,..., ~ v k } . Show that one of the ~ v i can be written as a linear combination of the others. (Yes, we did this in class; write it up carefully.) Is it true that any of the ~ v i can be written this way? *3. Let A be an n × n matrix. Show that the following are equivalent: a.
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This homework help was uploaded on 01/23/2008 for the course MATH 253 taught by Professor Ghitza during the Fall '07 term at Colby.

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253Homework5 - ma253, Fall 2007 - Problem Set 5 This...

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