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MATH 254 HW 8 - the same output vector i If so give an...

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MATH 254, FALL 2009 HOMEWORK 8 DUE THURSDAY, NOVEMBER 5 TH Part One of this assignment is due TUESDAY November 2 nd , and part two of this assignment is due at the beginning of class, Thursday, 11/05/09. You must bring a copy to class—it can be typed or neatly hand-written. If necessary, add illustrations by hand or with computer graphics. Late homework is not accepted. P ART O NE Complete the worksheet entitled, “One-to-One and Onto: Further Explorations” and bring it to class with you on Tuesday, November 2 nd . I will collect this on Tuesday and grade it based on completion and thoughtful effort. P ART T WO 1. Consider the transformation T: R 2 R 2 defined by T x y = y x . a. Describe in words and/or graphically how this transformation affects vectors/the space. b. Find the standard matrix A that defines this transformation. c. Under this transformation, is it possible to find two different input vectors that will give
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Unformatted text preview: the same output vector? i. If so, give an example. ii. If it is not possible, explain why not. d. Is the transformation onto? Explain. e. Is A invertible? If so, find A-1 . If not, explain why. f. What is the column space of A ? g. What is the null space of A ? 2. Section 1.9, #16. 3. Section 1.9, #18. (Note: The book has written their transformation a little differently than I have been doing on the board. What they have is the same as: T x 1 x 2 = 2 x 2 − 3 x 1 x 1 − 4 x 2 x 2 . The task is to find a matrix A that implements this transformation.) 4. Determine if the transformation from 1.9 #18 is (a) one-to-one and (b) onto. Justify each answer. 5. Section 2.3, #4 6. Section 2.3, #6 7. Section 2.8, #8 8. Section 2.8, #28 9. Section 2.8, #29 10. Section 4.2, #2 11. Section 4.2, #4 12. Section 4.2, #24...
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