e611k - your lowest quiz grade, nor the MHW. See the upper...

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MAS 3105 March 24, 2011 Quiz 6 and Key Prof. S. Hudson 1) Let S be the subspace of R 3 spanned by x = (2 , 1 , 1) T . Find a basis of S . 2) In C [0 ] with inner product R π 0 fg dx , compute h e 2 x ,e - 2 x i . 3) Choose ONE of these. a) Prove thm 5.1.1; that for nonzero vectors x , y R 2 , x T y = || x || || y || cos( θ ). b) Thm 5.3.2: If A has rank n , then the normal equations have a unique solution. c) Derive the normal equations, used to solve least squares problems. Remarks and Answers: The Q6 average was about 42 / 60, with mostly good scores on problems 1 and 2, but very mixed results on the proof. The scale for Q6 is: A’s 46 to 60 B’s 40 to 45 C’s 34 to 39 D’s 28 to 33 F’s 0 to 27 I’ve updated your estimated semester grade, including this quiz and HW1-6, but not
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Unformatted text preview: your lowest quiz grade, nor the MHW. See the upper right corner. If you opted out of the HW, your average may be inaccurate [I subbed HW=80, for now]. Answers: 1) You were supposed to use the F.S.Thm from Ch.5.2. But most people used ad hoc methods and did OK. One answer is { [-1 , 1 , 1] T , [0 , 1 ,-1] T } . Every good answer should include two vectors, by the theorem, dim S + dim S ⊥ = n = 3. 2) π 3) See the text. Both b and c were announced. The proof of b could use the textbook proof, but was also one of your previous hw’s. 1...
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This note was uploaded on 12/26/2011 for the course MAS 3105 taught by Professor Julianedwards during the Spring '09 term at FIU.

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