Fall2011-HW8-soln - Homework 8 Solution Math 371, Fall 2011...

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Unformatted text preview: Homework 8 Solution Math 371, Fall 2011 Assigned: Thursday, November 3, 2011 Due: Thursday, November 10, 2011 Clearly label all plots using title , xlabel , ylabel , legend Use the subplot command to compare multiple plots Include printouts of all Matlab code, labeled with your name, date, and section. Add 12 for page numbers in the international edition. (1) Which of the following matrices is symmetric positive definite? Explain your answer. (a) 2 1 1 4 (b) 2- 1- 1 4 (c) 1 / 2- 1- 1 1 / 2 (d) 10 1 1 1 10 1 1 1- 1 Let A denote the matrix and let x = x 1 x 2 in the first three parts. We then have (a) x T Ax = 2 x 2 1 + 2 x 1 x 2 + 4 x 2 2 = x 2 1 + ( x 1 + x 2 ) 2 + 3 x 2 2 which is obviously positive for all nonzero x : spd. (b) x T Ax = 2 x 2 1- 2 x 1 x 2 + 4 x 2 2 = x 2 1 + ( x 1- x 2 ) 2 + 3 x 2 2 which is obviously positive for all nonzero x: spd. (c) x T Ax = x 2 1 / 2- 2 x 1 x 2 + x 2 2 / 2 = ( x 1- 2 x 2 ) 2 / 2- 7 x 2 2 / 2. This quantity is negative if2....
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Fall2011-HW8-soln - Homework 8 Solution Math 371, Fall 2011...

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