Diagonalize the quadratic forms in Exercises 3540 by finding an orthogonal matrix Q such

Linear Algebra: A Modern Introduction (Available 2011 Titles Enhanced Web Assign) | 3rd Edition | ISBN: 9780538735452 | Authors: David Poole

ISBN: 9780538735452 298

Solution for problem 5.5.31 Chapter 5

Linear Algebra: A Modern Introduction (Available 2011 Titles Enhanced Web Assign) | 3rd Edition

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Linear Algebra: A Modern Introduction (Available 2011 Titles Enhanced Web Assign) | 3rd Edition

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Problem 5.5.31

Diagonalize the quadratic forms in Exercises 3540 by finding an orthogonal matrix Q such that the change of variable x Qy transforms the given form into one with no cross-product terms. Give Q and the new quadratic form.

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Step 1 of 3

MAT 211 Lecture 6 15.3 & 15.4 Section 15.3 Homework #8: ln(x,y)= x +y2yx2 lnx= 0 & lny= 0 1st Derivative: lnx= 2xy lny= 2y2yx I. 2xy=0 > x=1 2y=0 2=y y= 2 2 2y2yx=0 > y=0 2xy =0 2x0=0 x=0 II. 2y(1x)= 0 y=0 & x=1 Critical Points: (0,0); (1, 2); (1, + 2) 2nd Derivative: lnxx= 2 lnxx (0,0)= 2 lnyy= 22x lnyy (0,0)= 2 lnxy= 2y lnxy (0,0)= 0 H(0,0)= 2 * 2 0= 4 Since lnxx= 2>0, then we have a relative minimum at (0,0). Critical point at (1, 2) : lnxx (1, 2) =2 √ lnyy (1, 2) =0 lnxy (1, 2) =(2)( 2) = 2 2 2 H (1, 2)= 2 * 0 (2 2) 08= 8< 0 Since H is negative, we have a saddle point at (1, 2). Critical point at (1, + 2) : lnxx (1, + 2)=2 lnyy (1, + 2)=0 lnxy (1, + 2)= 2( 2) 2 H(1, + 2) = 2* 0 (2 2)= 08= 8<0 Since H is negative, we have a saddle point at (1, + 2). Homework #11: M(c,f)= 11+8c+4c 240f20cf+40f2 Mc= 8+8c20f> 8+8c20f= 0 divide by 4 2+2c5f=0 Mf= 4020c+80f> 4020c+80f=0 divide by 20 2c+4f=0

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Chapter 5, Problem 5.5.31 is Solved

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Textbook: Linear Algebra: A Modern Introduction (Available 2011 Titles Enhanced Web Assign)

Edition: 3

Author: David Poole

ISBN: 9780538735452

The full step-by-step solution to problem: 5.5.31 from chapter: 5 was answered by , our top Math solution expert on 01/29/18, 04:03PM. The answer to “Diagonalize the quadratic forms in Exercises 3540 by finding an orthogonal matrix Q such that the change of variable x Qy transforms the given form into one with no cross-product terms. Give Q and the new quadratic form.” is broken down into a number of easy to follow steps, and 38 words. This full solution covers the following key subjects: . This expansive textbook survival guide covers 7 chapters, and 1985 solutions. Since the solution to 5.5.31 from 5 chapter was answered, more than 240 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Linear Algebra: A Modern Introduction (Available 2011 Titles Enhanced Web Assign), edition: 3. Linear Algebra: A Modern Introduction (Available 2011 Titles Enhanced Web Assign) was written by and is associated to the ISBN: 9780538735452.