quiz1_18085f07

quiz1_18085f07 - MIT OpenCourseWare http/ocw.mit.edu 18.085...

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Unformatted text preview: 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 . 18.085 Quiz 1 October 5, 2007 Professor Strang Your PRINTED name is: Grading 1 2 3 1) (39 pts.) With h = 1 1 2 there are 4 meshpoints , , , 1 and displacements u , u 1 , u 2 , u 3 . 3 3 3 a) Write down the matrices A , A 1 , A 2 with three rows that produce the first differences u i − u i − 1 : A has boundary conditions on u A 1 has 1 boundary condition u = (left end fixed) A 2 has 2 boundary conditions u = u 3 = 0. b) Write down all three matrices A T A , A T 1 A 1 , A T 2 A 2 . CROSS OUT IF FALSE / GIVE REASON BASED ON COLUMNS OF A ! K = A T A is (singular) (invertible) (positive definite) Reason: K 1 = A T 1 A 1 is (singular) (invertible) (positive definite) Reason: c) Find all solutions w = ( w 1 , w 2 , w 3 ) to each of these equations: A T w = 0 A 1 T w = 0 A 2 T w = 0 1 2) (33 pts.) a)...
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quiz1_18085f07 - MIT OpenCourseWare http/ocw.mit.edu 18.085...

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