Unformatted text preview: x 12 x 3 + x 4 = 4 Use fractions throughout your calculations. 3. Let A = 1 0 31 1 2 2 1 . (a) Find (by hand) the LU factorization of A (without pivoting). (b) Use the LU factorization from (a) to ﬁnd the solution to Ax = b where b = [10 1 20] T . (c) Use the LU factorization from (a) to ﬁnd the determinant of A . 4. Let A = 60 10 2. 1 . 4 60 102 . (a) Find  A  1 ,  A  ∞ and  A  f (by hand). (b) Use Matlab to ﬁnd  A  2 , and also to check your answers in part (a). Provide a printout or writeup of the commands entered in Matlab, as well as of the output obtained. (c) Using Matlab, ﬁnd the condition number of A based on the 2norm. Do you expect the system Ax = b to be illconditioned? Explain. (Note: Material from Question 4 will not be covered on Test 1, but will be covered on Test 2)...
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 Winter '12
 Dr.SilvanaIlie
 Numerical Analysis, LU factorization

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