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Unformatted text preview: _Second 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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 Winter '08
 R.Schmidt

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