Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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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 =
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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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