Unformatted text preview: for full credit. 2) I gave at least 10 points if you knew the normal equations and substituted into them successfully. Solving the system involves some fractions; the simplest method is probably to compute the inverse of A T A using the adjoint method. A T A ˆ x = A T b becomes ± 977 11 ²± x 1 x 2 ² = ± 5 4 ² So , ± x 1 x 2 ² = 1 50 ± 11 7 7 9 ²± 5 4 ² = ± 83 / 50 71 / 50 ² 3) Most people chose a) or c); see the text. In a), you should explain why R ( A T ) ⊥ N ( A ) (see the paragraph above Theorem 5.2.1). I can see how you might think this wasn’t part of the proof, so I only took oﬀ about 2 points for that. You are always welcome to ask me about such things before or during the quiz. Likewise, part c) was Problem 5.2.13, parts a thru c. Explain why N ( A T A ) = N ( A ). 1...
View
Full Document
 Spring '09
 JULIANEDWARDS
 Linear least squares, upper right corner, Prof. S. Hudson, Fundamental Subspace Theorem

Click to edit the document details