Homework Help is Here – Start Your Trial Now!
Math
Calculus
Find an orthogonal change of variables that eliminates the cross product terms in the quadratic form Q, and express Q in terms of the new variables. 7x + 6x3 + 5x – 4x1.x2 + 4x2x3 2 A substitution x = Py that eliminates cross-product terms is x =-yı + y2 - „¥3, X2 = –; 1 2 2 1 2 32 + 3Y3, 2 2 1 X3 = -y1 + Y2 – ¬V3. The new quadratic form is 3y – 6y + 9y. 3 O A substitution x = Py that eliminates cross-product terms is x1 = - yı+ 2y2 - 2y3, x2 = - 2y1 + Y2 + 2y3, X3 = 2y1 + 2y2 + y3. The new quadratic form is 3y + 6y + 9y. 1 A substitution x = Py that eliminates cross-product terms is x = - 2 2 V2 - 2 1 yi +y2 + X2 = - 2 2 1 X3 = 7Y1 + y2+ V3. The new quadratic form is 3y + 6y} + 9y?. 2 A substitution x = Py that eliminates cross-product terms is x = - 1 VI - 2 2 2 Yi +z2 +V3. The new quadratic form is 6y + 5y + 3y. 1 X3 = 7V1 O A substitution x = Py that eliminates cross-product terms is x1 = - y1 - 2y2 - 2y3, X2 = - 2y1 - Y2+ 2y3, X3 = 2y1 + 2y2 +y3. The new quadratic form is 9y + 3y + 6y?.

Find an orthogonal change of variables that eliminates the cross product terms in the quadratic form Q, and express Q in terms of the new variables. 7x + 6x3 + 5x – 4x1.x2 + 4x2x3 2 A substitution x = Py that eliminates cross-product terms is x =-yı + y2 - „¥3, X2 = –; 1 2 2 1 2 32 + 3Y3, 2 2 1 X3 = -y1 + Y2 – ¬V3. The new quadratic form is 3y – 6y + 9y. 3 O A substitution x = Py that eliminates cross-product terms is x1 = - yı+ 2y2 - 2y3, x2 = - 2y1 + Y2 + 2y3, X3 = 2y1 + 2y2 + y3. The new quadratic form is 3y + 6y + 9y. 1 A substitution x = Py that eliminates cross-product terms is x = - 2 2 V2 - 2 1 yi +y2 + X2 = - 2 2 1 X3 = 7Y1 + y2+ V3. The new quadratic form is 3y + 6y} + 9y?. 2 A substitution x = Py that eliminates cross-product terms is x = - 1 VI - 2 2 2 Yi +z2 +V3. The new quadratic form is 6y + 5y + 3y. 1 X3 = 7V1 O A substitution x = Py that eliminates cross-product terms is x1 = - y1 - 2y2 - 2y3, X2 = - 2y1 - Y2+ 2y3, X3 = 2y1 + 2y2 +y3. The new quadratic form is 9y + 3y + 6y?.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter9: Quadratic Functions And Equations
Section9.3: Solving Quadratic Equations By Graphing
Problem 35PPS
See similar textbooks
icon
Related questions
Question
Find an orthogonal change of variables that eliminates the cross product terms in the quadratic form Q, and express Q in terms of the new variables. 7x구 +6x2 + 5x금-4r x2 + 4x2.13 2 A substitution x = Py that eliminates cross-product terms is xį = -y1 +Y2 - V3, x2 = -z1 + zy2 +zV3, 2 1 X3 = -V1 + V2 – V3. The new quadratic form is 3y – 6y + 9y?. O A substitution x = Py that eliminates cross-product terms is x1 = - y1+ 2y2 - 2y3, X2 = - 2y1+ y2+ 2y3, X3 = 2y1+2y2 + y3- The new quadratic form is 3y + 6y + 9y. 2 1 + 2 2 A substitution x = Py that eliminates cross-product terms is x = - 2 X2 = 1 + + 1 V2 + zV3. The new quadratic form is 3y + 6y + 9y. X3 = 1 2 2 2 A substitution x = Py that eliminates cross-product terms is x = -I -2 -y3, x2 = -1 - 32 + 33, 2 1 X3 = 7Y1 + zV2 + V3. The new quadratic form is 6y+ 5y + 3y. O A substitution x = Py that eliminates cross-product terms is x1 = - y1- 2y2 - 2y3, X2 = - 2y1 – Y2+ 2y3, X3 = 2y1+2y2 + y3- The new quadratic form is 9y + 3y + 6y.
Transcribed Image Text:Find an orthogonal change of variables that eliminates the cross product terms in the quadratic form Q, and express Q in terms of the new variables. 7x구 +6x2 + 5x금-4r x2 + 4x2.13 2 A substitution x = Py that eliminates cross-product terms is xį = -y1 +Y2 - V3, x2 = -z1 + zy2 +zV3, 2 1 X3 = -V1 + V2 – V3. The new quadratic form is 3y – 6y + 9y?. O A substitution x = Py that eliminates cross-product terms is x1 = - y1+ 2y2 - 2y3, X2 = - 2y1+ y2+ 2y3, X3 = 2y1+2y2 + y3- The new quadratic form is 3y + 6y + 9y. 2 1 + 2 2 A substitution x = Py that eliminates cross-product terms is x = - 2 X2 = 1 + + 1 V2 + zV3. The new quadratic form is 3y + 6y + 9y. X3 = 1 2 2 2 A substitution x = Py that eliminates cross-product terms is x = -I -2 -y3, x2 = -1 - 32 + 33, 2 1 X3 = 7Y1 + zV2 + V3. The new quadratic form is 6y+ 5y + 3y. O A substitution x = Py that eliminates cross-product terms is x1 = - y1- 2y2 - 2y3, X2 = - 2y1 – Y2+ 2y3, X3 = 2y1+2y2 + y3- The new quadratic form is 9y + 3y + 6y.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Linear Equations
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Glencoe Algebra 1, Student Edition, 9780079039897…
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell
Functions and Change: A Modeling Approach to Coll…
Functions and Change: A Modeling Approach to Coll…
Algebra
ISBN:
9781337111348
Author:
Bruce Crauder, Benny Evans, Alan Noell
Publisher:
Cengage Learning
College Algebra
College Algebra
Algebra
ISBN:
9781337282291
Author:
Ron Larson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS