Classify the quadratic form below. Then make a change of variable, x = Py, that transforms the quadratic form into one with no cross-product terms. Write the new quadratic form. -x²-3x2 - 6x2 - 6x-2x₁x₂ + 2x₁ x3 + 2x₁ x4 +6×3×4
Classify the quadratic form below. Then make a change of variable, x = Py, that transforms the quadratic form into one with no cross-product terms. Write the new quadratic form. -x²-3x2 - 6x2 - 6x-2x₁x₂ + 2x₁ x3 + 2x₁ x4 +6×3×4
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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Question
![Classify the quadratic form below. Then make a change of variable, x = Py, that
transforms the quadratic form into one with no cross-product terms. Write the new
quadratic form.
-x²-3x2 - 6x2 - 6x² - 2x₁ x2 + 2x₁ x3 +2×₁ X4 +6×3×4
Classify the given quadratic form.
OA. Negative definite
B. Positive semidefinite
c. Negative semidefinite
D. Indefinite
OE. Positive definite
The new quadratic form is y¹ Dy=.
(Simplify your answer.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffc812dba-7b16-4346-a82c-4239f2a0408a%2F6f287109-9a93-4e72-ab79-4a8de0ee92ca%2F0mt17yt_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 terms. Write the new
quadratic form.
-x²-3x2 - 6x2 - 6x² - 2x₁ x2 + 2x₁ x3 +2×₁ X4 +6×3×4
Classify the given quadratic form.
OA. Negative definite
B. Positive semidefinite
c. Negative semidefinite
D. Indefinite
OE. Positive definite
The new quadratic form is y¹ Dy=.
(Simplify your answer.)
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