MRQ3 - UCSC AMS 10 FALL 2009 Final Review Questions Note:...

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Unformatted text preview: UCSC AMS 10 FALL 2009 Final Review Questions Note: The final exam is comprehensive, but these questions only cover chapters 5 and 6. To prepare for the final exam, you need to review all three sets of review questions (as well as the homework, class notes, etc.). (1) Consider the subspace of R 4 : V = span 1 2 3 1 , 1- 1 1- 1 . a. Find an orthogonal basis for V . b. Find an orthonormal basis for V . c. Find the projection of b = 2 6 4 1 1 1 1 3 7 5 onto the subspace V . d. Find a basis for V , the orthogonal complement of V in R 4 . (2) Find the vector in W = span 1 1 2 , 2 1- 1 that is closest to the vector b = 2 3 5 . (3) Find the least-squares solution to the system x + 2 y = 4 2 x- y = 2 x- y = 1- x + y = 3 (4) Find the equation y = ax + b of the least-squares line that best fits the given data points: (1 , 1) , (2 , 1) , (4 , 3)...
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MRQ3 - UCSC AMS 10 FALL 2009 Final Review Questions Note:...

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