Math

Assignment 1

Math 240 (Summer 2010)

Due Friday, May 21, 2010

A complete assignment consists of the following: • A filled in cover sheet (available from WebCT) • The answer to the Instructor’s Question • The completed preliminary questions. Late assignments, unstapled assignments, assignment without cover pages, assignments left in the incorrect box or copied assignments will not be accepted and will receive a grade of zero. Some suggestions for making the most of homework problems: • Do rough work on scratch paper. • If you find one solution, try to find another (a simpler solution may reveal itself). • When you find a solution, try to see it as a whole without all the little details.

Question type and comments table:

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mechanics of writing proofs get a good grasp of spans exploring row reduction concepts exploring row reduction concepts row reduction vocabulary exploring row reduction concepts using row reduction these acronyms mean.

Preliminary questions: 1. Prove that the elementary row operation of scaling is reversible. 2. Find the general solution to the system whose  2 1 −1 −2 3 −1 4 1 −2 1 augmented matrix is  3 1 1

3. Lay 1.1: 20, 22. Lay 1.2: 4, 20. Lay 1.3: 14, 21. Instructor’s question: Let W be the set of vectors of the form a. Is it true that W = span 1 0 , −1 1 ? a . −a

Justify your answer. Hint: check separately whether every vector in W is in the span on the right hand side and that every vector in the span on the right hand side is in W b. Is it true that W = span Justify your answer. c. Is it true that W = span Justify your answer. −2 1 , 2 −1 ? 1 −1 ?

Legend (for “type” of...