Midterm_sample

Midterm_sample - MAE 107 Computational Methods Summer...

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MAE 107 – Computational Methods Summer Session II 2009 Midterm sample Guidelines : This is a closed book and closed notes exam. No calculator or computer allowed . Clearly explain your answers to each of the question and write your solution neatly. Detail all necessary intermediate steps and clearly identify your final answers (e.g. box them in). Do not forget to put your name and student ID on your test and staple/attach all the pages together. Problem 1 Write a short Matlab function that takes only one argument n and returns the factorial of n for n 0 (remember the convention 0! = 1). Problem 2 Consider the matrix A = 2 - 1 3 - 2 - 2 - 2 2 - 7 4 . 1. Obtain the LU decomposition of A using Gauss elimination without partial pivoting. 2. Using this decomposition, compute the determinant of A . 3. Using the LU decomposition, compute the matrix Y = A - 1 . 4. Check your result using the direct formula for the inverse of a square matrix.
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