quiz2f07

# quiz2f07 - MIT OpenCourseWare http/ocw.mit.edu 18.085...

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MIT OpenCourseWare http://ocw.mit.edu 18.085 Computational Science and Engineering I Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .

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18.085 Quiz 2 November 2, 2007 Professor Strang Your PRINTED name is: Grading 1 2 3 1) (40 pts.) This problem is based on a 5-node graph. I have not included edge numbers and arrows. Add them if you want to: not needed. (a) Find A T A for this graph. A is the incidence matrix. (b) The sum of the eigenvalues of A T A is . The product of those eigenvalues is . (c) What is A T A for a graph with only one edge ? How can that small A T A be used in constructing A T A for a large graph ? (d) Suppose I want to solve Au = ones(8 , 1) = b by least squares. What equation gives a best u ? For the incidence matrix A , is there exactly one best u solving that equation ? (If your equation has more than one best u , describe the diﬀerence between any two solutions.) 1 2 3 4 5

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## This note was uploaded on 04/12/2011 for the course MATH 18.085 taught by Professor Staff during the Fall '10 term at MIT.

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quiz2f07 - MIT OpenCourseWare http/ocw.mit.edu 18.085...

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