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

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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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
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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