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Unformatted text preview: 1 1 1 and 13 2 , and let y = 143 . Write y as the sum of a vector in W and a vector orthogonal to W . 5. (10 points) Find an orthogonal basis for the column space of A = 1 22 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 ﬁt a parabola y = β + β 1 x + β 2 x 2 to the data (0 , 2) , (1 , 6) , (3 , 26) , (4 , 50). Give a matrix X and a vector y so that the equation X β β 1 β 2 = y leads to a leastsquares ﬁt of the parabola with the given data. 7. (8 points) Find a leastsquares solution of 1 5 3 12 4 x = 21 5 ....
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This note was uploaded on 01/28/2009 for the course M 340L taught by Professor Pavlovic during the Fall '08 term at University of Texas.
 Fall '08
 PAVLOVIC
 Matrices

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