253Homework2

# Linear Algebra with Applications (3rd Edition)

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ma253 , Fall 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 satisfied.) 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 5 . *3. Read definition 4 . 1 . 1 on page 153 ; this defines the abstract notion of a linear space as we did it in class. Suppose V is a linear space and v is an element of
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