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Unformatted text preview: x 1-2 x 3 + x 4 = 4 Use fractions throughout your calculations. 3. Let A = 1 0 3-1 1 2 2 1 . (a) Find (by hand) the LU factorization of A (without pivoting). (b) Use the LU factorization from (a) to nd the solution to Ax = b where b = [10 1 20] T . (c) Use the LU factorization from (a) to nd the determinant of A . 4. Let A = -60 10 2-. 1 . 4 60 10-2 . (a) Find || A || 1 , || A || and || A || f (by hand). (b) Use Matlab to nd || A || 2 , and also to check your answers in part (a). Provide a print-out or write-up of the commands entered in Matlab, as well as of the output obtained. (c) Using Matlab, nd the condition number of A based on the 2-norm. Do you expect the system Ax = b to be ill-conditioned? 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
- Numerical Analysis