Exam1-1997 - CHEE 3334 Fall '97 EXAM 1 Michael Nikolaou...

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CHEE 3334 Fall ’97 Michael Nikolaou EXAM 1 Open-book, open-notes. Total points 100. Please, budget your time ! Do NOT try to read the book during the exam! Write neatly! Do NOT use your programmable calculator to find results you are asked to compute in a certain way--after all, the calculator may find the wrong answer or not all answers! Show all work. Return this sheet with your exam . GOOD LUCK! 1. You are given the matrix = 9 8 7 6 5 4 3 2 1 A (1) (10 pts.) (a) Find an LU decomposition for A . (10 pts.) (b) Show how the above factors L and U can be used in forward and back-substitution, to solve the system of equations Ax = b , where T b ] 6 3 0 [ = (2) (Show your work. Do not merely give the solution of Ax = b .) (10 pts.) (c) Use the results of part (a) to calculate the determinant of A . (Show your work. Do not merely give the value of the determinant of A .) 2. You are given the system of equations = 1 1 4 3 2 1 2 1 x x (3) (10 pts.) (a) Perform one iteration of the Gauss-Seidel method with the initial guess = 1 1 ) 0 ( 2 ) 0 ( 1 x x . (4) (10 pts.) (b) Will the Gauss-Seidel method applied to the above equation (3) have guaranteed convergence?
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Exam1-1997 - CHEE 3334 Fall '97 EXAM 1 Michael Nikolaou...

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