MIdtermFall2008Math6643

MIdtermFall2008Math6643 - Math 6643 Midterm Exam Fall 2008...

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Math 6643 Midterm Exam Fall 2008 Name: 80 minutes, 5 questions for 50 points total. No calculators or notes permitted. Only the  textbook for the course and a pen is permitted. No credit is given for answers without the  reasoning that leads to them: show all work. If you need more paper, raise your hand. 1. (10 points) Let A = [ 1 1 ] . Compute the reduced SVD of A. Hint: consider the eigenvalue problem for A * A.
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2. Let A = [ 2 1 ] . a. (6 points) Find the orthogonal projector onto the range of A . b. (4 points) Find x which minimizes ∣∣ b Ax ∣∣ 2 (a least squares problem), where b = [ 1 1 ] .
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3. a. (12 points) Find the QR factorization of A = [ 1 0 1
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MIdtermFall2008Math6643 - Math 6643 Midterm Exam Fall 2008...

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