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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 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
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 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.)
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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