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August 11th, 2012, 03:52 PM  #1 
Newbie Joined: Jul 2012 Posts: 6 Thanks: 0  Best leastsquares approximation
Given the subspace =\begin{bmatrix} x_1\\x_2\\x_3\end{bmatrix}, x_12x_2+x_3=0\}" /> and the vector Find a basis for the indicated subspace W. For the given vector v, solve the normal equations and determine the best approximation w*. Verify that vw* is orthogonal to the basis vectors. I know how to find the basis and check orthogonality, and I know how to solve for w* using an orthogonal basis and how to get an orthogonal basis, but I don't understand how the normal equation is used to solve for w*. According to my textbook the normal equation is . If I understand it correctly, Ax=w* and b = v so it should be I get the feeling I'm missing something obvious and I'm using the wrong equation because can't be constructed without more information can it? 
August 12th, 2012, 02:26 PM  #2 
Newbie Joined: Jul 2012 Posts: 6 Thanks: 0  Re: Best leastsquares approximation
I figured out what I was supposed to do. It took me forever to think to use the subspace as a constraint for the system of equations to solve for w*.


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approximation, leastsquares 
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