This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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....
View
Full
Document
This note was uploaded on 12/16/2011 for the course MATH 371 taught by Professor Krasny during the Fall '08 term at University of Michigan.
 Fall '08
 KRASNY
 matlab

Click to edit the document details