2107test4_09

# 2107test4_09 - 2 2 2 1 2 1 4 x x x x q = and orthogonally...

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MATH 2107A TEST 4 NOVEMBER 20, 2009 1 of 4 This test has 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.

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MATH 2107A TEST 4 NOVEMBER 20, 2009 2 of 4 EXTRA PAGE FOR ROUGH WORK
MATH 2107A TEST 4 NOVEMBER 20, 2009 3 of 4 2. (a)[10] Find the matrix of the quadratic form

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Unformatted text preview: 2 2 2 1 2 1 4 x x x x q + + = and orthogonally diagonalize it. (b) [3] Find a change of variable that will transform the quadratic form into one with no cross products. What is the new quadratic form? MATH 2107A TEST 4 NOVEMBER 20, 2009 4 of 4 3.(a)[6] Let ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ = 3 2 2 3 A and Aw v w v T = , defines an inner product on 2 ℜ . Let ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ = 4 3 v and ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ = 1 2 w . Compute v , w and the distance between v and w . (b)[3] Let 1 = u , 2 = v , 3 = w , 1 , − = v u , , = w u and 3 , = w v . Compute v u w v − + 2 ,...
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2107test4_09 - 2 2 2 1 2 1 4 x x x x q = and orthogonally...

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