midtermsolutions205f

midtermsolutions205f - Midterm 2, Math 33A, Fall 2005...

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Unformatted text preview: Midterm 2, Math 33A, Fall 2005 November 18, 2005 Name: UCLA ID: Section (circle one): 1A Alex Chen Tuesday 1B Alex Chen Thursday 1C Michael VanValkenburgh Tuesday 1D Michael VanValkenburgh Thursday Directions: Fill in your name and circle your section above. Do not turn the page until instructed to do so. You have 50 minutes to complete the exam. No outside materials are allowed; use only your brain and a writing instrument. There are 3 problems; each is worth 10 points total. Extra scratch paper is included. If your work on a problem appears on a different page, indicate clearly where it may be found. Show all the necessary steps involved in finding your solutions, unless otherwise instructed. In the interest of us not losing pages of your exam, please refrain from detaching pages from the exam. Good luck. Problem Score 1 2 3 Total 1 1. Indicate whether each statement is true or false. There is no need to justify your answers here. (2 pts) There exists a 3 by 5 matrix A whose kernel is spanned by the vector 1 1 1 1 1 . T F False. By the rank-nullity theorem, we must have dimimageA + dim ker A = 5. If the statement is true, then dim ker A = 1, and thus dim imageA = rankA = 4. But this is impossible for a 3 by 5 matrix. (2 pts) If A and B are symmetric matrices, then so is AB . T F . False. If A = 0 1 1 0 and B = 1 0 0 0 , then AB = 0 0 1 0 . A and B are symmetric but AB is not....
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This note was uploaded on 04/02/2008 for the course MATH 33a taught by Professor Lee during the Fall '08 term at UCLA.

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midtermsolutions205f - Midterm 2, Math 33A, Fall 2005...

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