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18.02 Pset 1

# 18.02 Pset 1 - 18.02 HOMEWORK#1 DUE BJORN POONEN Page...

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18.02 HOMEWORK #1, DUE SEPTEMBER 16, 2010 BJORN POONEN Page numbers refer to Edwards & Penney. Problem numbers like 1A-1 refer to the Sup- plementary Notes. “(After Sept. 10)” means that the math needed for the problem should have been covered in lecture by that date. Make sure that you know how to do all exercises listed, but hand in only those labelled with point values . 1. Part A (After Sept. 9) p. 777: 21, 31 (After Sept. 9) p. 786: 13* (for the vectors in 1 only) (5 pts.), 39, 58* (10 pts.), 70* (5 pts.) (After Sept. 9) 1A-1b, 1A-5, 1A-8, 1A-12* (10 pts.) (After Sept. 9) 1B-1b, 1B-3b, 1B-6 (in c, change “empty” to “a point”), 1B-8, 1B-12 (After Sept. 9) 1C-2b, 1C-3b, 1C-7, 1C-9 (After Sept. 10) 1D-1a, 1D-3, 1D-5 (After Sept. 10) 1F-5a, 1F-8a, 1F-11b* (10 pts.) (After Sept. 14) 1G-2a, 1G-3, 1G-4 (After Sept. 14) 1H-3(a,c), 1H-6* (10 pts.), 1H-8* (10 pts.) 2. Part B B.1) (After Sept. 10, 15 pts.) A nilpotent matrix is a square matrix A such that A n = 0 for some positive integer
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