q118085f03

# q118085f03 - 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 1 Professor Strang October 6, 2003 Your name is: Grading 1 2 3 Total 1) (30 pts.) A system with 2 springs and nlasses is fixed-free. Co~lstantsare cl; c2. u, = 0 (a) Write down the matrices A and K = ATCA. (b) Prove by two tests (pivots, determinant,^, independence of columns of 4) that this matrix K is (positive definite) (positive semidefinite). Tell me which two tests you are using! 1 (c) hIultiply colunln times row to compute the "element matrices" Iil, K2: c2 Compute h; (column 1 of 4T)(~1)(ro~ = 1 of A) Compute h; (column 2 of 4T)(~2)(ro~ = 2 of A) Then K = K1 + 1c2.What vect,ors solve K2 For those displacements .rl and q, what is the energy in spring 2?

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2) (33 pts.) A network of nodes and edges and t,heir conductances cj > 0 is drawn without arrows. Arrows don't affect the answers to this problem; the edge
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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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q118085f03 - MIT OpenCourseWare http:/ocw.mit.edu 18.085...

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