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Unformatted text preview: U. Washington AMATH 352  Winter 2010 TakeHome Final Exam  Due on Monday March 15th, 2010 You may use books, your own previous homework assignments, and other resources. You may consult with the instructor or the assistants but not with other people. Do not work together. Questions about exercises 1, 2, 3, 4, 5, 10, and 11 will not be answered. 1. (5 points) Let A = 1 2 3 4 5 6 B = 1 1 1 1 If possible, compute the products AB and B T A T . Detail your computations. 2. (5 points) Prove that the function k x 1 x 2 k 1 =  x 1  +  x 2  satisfies the properties defining a norm. 3. (20 points) Consider the matrix A = 1 2 1 1 1 3 1 (a) Compute, by hand, the LU factorization with l ii = 1 (use row pivoting, if needed). (b) Compute, by hand, the QR factorization (with r ii > ). 4. (10 points) Check whether the following functions are linear. (a) x = x 1 x 2 R 2 , f ( x ) = x 1 x 2 x 2 x 1 (b) x = x 1 x 2 x 3 R 3 , f ( x ) = x 1 + 2 x 3 5. (10 points) Check whether the following sets are real linear spaces. When the set is a real5....
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 Winter '07
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