Classify the quadratic form below. Then make a change of variable, x= Py, that transforms the quadratic form into one with no cross-product term. Write the new quadratic form. 12x₁2 + 12x₂² + 12x3² + 12x4² +24x₁x₂ +24x3x4-32X1X4+32X₂X3 What is the most precise classification for the quadratic form? OA. Negative definite OB. Positive semidefinite OC. Negative semidefinite OD. Indefinite O E. Positive definite The new quadratic form is y Dy=0
Classify the quadratic form below. Then make a change of variable, x= Py, that transforms the quadratic form into one with no cross-product term. Write the new quadratic form. 12x₁2 + 12x₂² + 12x3² + 12x4² +24x₁x₂ +24x3x4-32X1X4+32X₂X3 What is the most precise classification for the quadratic form? OA. Negative definite OB. Positive semidefinite OC. Negative semidefinite OD. Indefinite O E. Positive definite The new quadratic form is y Dy=0
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter12: Quadratic Functions
Section12.4: Graphs Of Quadratic Equations: The Discriminant
Problem 2CE
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![Classify the quadratic form below. Then make a change of variable, x= Py, that transforms the quadratic form into one
with no cross-product term. Write the new quadratic form
12x₁2 + 12x₂² + 12x3² + 12x42 +24x₁x₂ +24x3x4-32x1x4 +32X₂X3
What is the most precise classification for the quadratic form?
OA. Negative definite
OB. Positive semidefinite
OC. Negative semidefinite
OD. Indefinite
O E. Positive definite
The new quadratic form is y Dy=0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fda68aaa6-bd6d-4479-a10c-a32228434cc1%2F718fd0b8-ebe7-4e19-8692-19f681903e27%2F31b3k0e_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Classify the quadratic form below. Then make a change of variable, x= Py, that transforms the quadratic form into one
with no cross-product term. Write the new quadratic form
12x₁2 + 12x₂² + 12x3² + 12x42 +24x₁x₂ +24x3x4-32x1x4 +32X₂X3
What is the most precise classification for the quadratic form?
OA. Negative definite
OB. Positive semidefinite
OC. Negative semidefinite
OD. Indefinite
O E. Positive definite
The new quadratic form is y Dy=0
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