253Homework1

# Linear Algebra with Applications (3rd Edition)

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ma253 , Fall 2007 — Problem Set 1 This problem set is about systems of linear equations and Gaussian elimination. As such, it includes several problems that are here just to help you practice the process. Most of those you need not turn in, but you should do them in order to make sure you have the method under control. So solve all the problems, then write up and turn in those marked with an asterisk. This assignment is due on Wednesday, September 19 . Remember that you should be able to do small row-reductions by hand, but that bigger ones are best done with technology: your calculator, the Linear Algebra Toolkit, or something else. See for more information. 1. Problems from the textbook: a. Section 1 . 1 , problems 5 , 7 , 9 , * 20 , * 28 . b. Section 1 . 2 , problems 5 , 11 , 13 , * 38 , * 44 , * 61 (this is an example of the “hundred fowls problem”). *2. Suppose we want to determine a quadratic curve (a curve whose equation is of degree two) on the plane. The curve is given by an equation a 1 x 2 + a 2 xy + a 3 y 2 + a 4 x + a 5 y

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