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Unformatted text preview: 1 1 1 and 1 32 , and let y = 1 4 3 . Write y as the sum of a vector in W and a vector orthogonal to W . 5. (8 points) Find an orthogonal basis for the column space of A = 1 2 2 1 1 1 . Then write down a matrix Q such that A = QR , where R is an invertible upper triangular matrix. Finally, write down a formula for R involving Q and A but DO NOT CALCULATE R. 6. (8 points) Suppose we want to t a parabola y = + 1 x + 2 x 2 to the data (0 , 1) , (1 , 5) , (2 , 14) , (3 , 25). Give a matrix X and a vector y so that the equation X 1 2 = y leads to a leastsquares t of the parabola with the given data. 7. (8 points) Find a leastsquares solution of 1 5 3 12 4 x = 423 ....
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 Fall '08
 PAVLOVIC

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