problems-1-223-F07

# problems-1-223-F07 - M ATH 223 P ROBLEM S ET 1 D UE 7 S EPT...

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M ATH 223 P ROBLEM S ET 1 D UE : 7 S EPT 4 S EPTEMBER 2007 It was my mistake about the due date on this. If you like, you may hand it in until Friday, 7 September, at my office in Malott with no penalty. Hereafter, problem sets will be due on Tuesdays in lecture. 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. § 1.1–1.3. Problems from the book: 1.1.4, 1.1.6 (d) & (g). 1.2.2, 1.2.6. 1.2.8, 1.2.11, 1.2.12, 1.2.22, 1.2.21, 1.2.23. 1.3.2, 1.3.5, 1.3.7, 1.3.12. Additional problems: 1. Suppose that A = bracketleftbigg a b c d bracketrightbigg is a matrix with integer entries. What condition(s) can you put on the entries a , b , c , and d to ensure that the inverse A - 1 also has integer entries? Is your condition necessary as well as sufficient? 2. Let - a = bracketleftbigg
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