253Homework2

Linear Algebra with Applications (3rd Edition)

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ma253 ,Fa l l 2007 — Problem Set 2 This problem set covers systems of linear equations and Gaussian elimination, basics of column vectors and R m , and a little bit about linear spaces. As usual, solve all the problems, then write up and turn in those marked with an asterisk. This assignment is due on Wednesday, September 26 . 1. Problems from the textbook: a. Section 1 . 1 , problem * 46 b. Section 1 . 2 , problem 50 ,* 53 . c. Section 1 . 3 , problems 1 , 2 ,* 4 , 13 , 15 , 17 ,* 19 , 20 ,* 21 ,* 22 ,* 24 , 38 , 46 , * 47 ,* 48 . *2. Decide whether each of these sets, with the natural operations, is a linear space. (All you need to do is to decide whether the conditions in 4 . 1 . 1 are all satis±ed.) You need not justify your answer. a. The space of all n -entry column vectors. b. The space of all m -entry row vectors. c. The space of all polynomials of degree 5 . d. The space of all polynomials of degree at most
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