Grunbaum MT2

Grunbaum MT2 - _-Se-cond midterm Exam-“of Math 54,; F3117...

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Unformatted text preview: _-Se-cond midterm Exam-“of Math 54,; F3117 2008 Oct 28th. 3:00—9:3oam ' Name _ SID 7 Section ancfiSI’s name NW 12mm Note: (-1) This is a closed book exam- No notes either. No calculators are allowed. All cellphones and other electronic devices should be 013’. Answers without explanation will not be accepted Make sure to in— clude your reasoning to get full credit. White neatly and if you need extra space use the back ofthe payee containing the problems. (3) This exam contained problems, each problem is worth the number of points indicated at the beginning of the problem. (4) Read all questions carefully before you start trying to answer them. ‘ Explain your answer. .2- (30 points) Givé’n the matrix - Find its eigenvalues. -- ' Find a matrix P and a diagonal matrix D such that AP 2 PD. Using the matrices P and D that you propose, compute seoaratelv AP and PD to check the identity. - <3. f-(30 points) GiVen the matrix (I/SQrtg} a sqrt(2)) 'A 2: _ .-1[3qrt(2) O 0 7 ' O 7 0". 1 Find. a QR fattorization of A 4; pOints)' 7 setting up and solving the appropriate ”n0rmal' ed113— ' :“tiOHS” find the equation 19' 2 1604—16133 7- .of the'least squares line that best'fits the data, points (2, 6), , (3, 7), (5,11), (8,20)- ' ...
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Grunbaum MT2 - _-Se-cond midterm Exam-“of Math 54,; F3117...

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