Fall2011-HW8-soln

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

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the 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.

### Page1 / 3

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online