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2107test4sol_09

# 2107test4sol_09 - MATH 2107A TEST 4 This test has two parts...

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MATH 2107A TEST 4 NOVEMBER 20, 2009 1 of 3 This test has two parts with a total of 30 marks. The test cannot be taken out from the examination room. Only nonprogrammable calculators are allowed. Show all your work. Duration: 50 minutes. NAME (in ink): STUDENT NO (in ink): 1. Let = 1 1 4 2 3 1 A and = 2 4 3 b (a) [4.5] Find the QR-factorization of the matrix A . (b)[3.5] Find the least square solution to the equation b AX = . (c) [2]Find the least square error in your solution. (a) The columns of A are = 1 2 1 1 C and = 1 4 3 1 C , They are not orthogonal. Using Gram-Schmidt algorithm, = = 1 2 1 1 1 C E (1/2 mark) and = = = 1 0 1 1 2 1 . 6 12 1 4 3 . . 1 1 1 1 2 2 2 E E E E C C E (1 mark) And 6 1 = E and 2 2 = E . So, we normalize the above orthogonal vectors. 1 1 1 E E Q = and 2 2 2 E E Q = .

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2107test4sol_09 - MATH 2107A TEST 4 This test has two parts...

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