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. 2 2 6x₁²2 +6x₂² +6x3² +6x4² + 12x₁×2 + 12×3×4 + 16x₁x4-16x2x3 What is the most precise classification for the quadratic form? O A. Positive semidefinite OB. Indefinite OC. Positive definite OD. Negative semidefinite OE. Negative definite T The new quadratic form is y' Dy=
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. 2 2 6x₁²2 +6x₂² +6x3² +6x4² + 12x₁×2 + 12×3×4 + 16x₁x4-16x2x3 What is the most precise classification for the quadratic form? O A. Positive semidefinite OB. Indefinite OC. Positive definite OD. Negative semidefinite OE. Negative definite T The new quadratic form is y' Dy=
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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.
2
2
6x₁ + 6x₂
2
+ 6x3
+ 12x1x2 + 12x3x4 + 16x₁x4-16x2x3
+ 6x4
What is the most precise classification for the quadratic form?
O A. Positive semidefinite
B. Indefinite
OC. Positive definite
OD. Negative semidefinite
OE. Negative definite
The new quadratic form is y' Dy =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1362bc0e-74c6-4c74-bcb9-cae15d132a85%2F53d17e71-b2af-44b2-bb1d-7cd0cb8ccd49%2Fz1wwuft_processed.png&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.
2
2
6x₁ + 6x₂
2
+ 6x3
+ 12x1x2 + 12x3x4 + 16x₁x4-16x2x3
+ 6x4
What is the most precise classification for the quadratic form?
O A. Positive semidefinite
B. Indefinite
OC. Positive definite
OD. Negative semidefinite
OE. Negative definite
The new quadratic form is y' Dy =
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