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. 2x² +6x₁x2 + 2x² Choose the most precise classification for the quadratic form. OA. Positive definite OB. Positive semidefinite OC. Negative semidefinite D. Indefinite OE. Negative definite The new quadratic form is y Dy=[ (Simplify your answer.)

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
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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.
2x² + 6x₁x₂ + 2x²
Choose the most precise classification for the quadratic form.
OA. Positive definite
OB. Positive semidefinite
OC. Negative semidefinite
D. Indefinite
E. Negative definite
The new quadratic form is y¹ Dy =
(Simplify your answer.)
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. 2x² + 6x₁x₂ + 2x² Choose the most precise classification for the quadratic form. OA. Positive definite OB. Positive semidefinite OC. Negative semidefinite D. Indefinite E. Negative definite The new quadratic form is y¹ Dy = (Simplify your answer.)
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