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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. 8x₁ +8x₂ 2 + 8x4² + 16x₁x₂ + 16×3×4 +30x₁x4-30x2x3 +8x3 What is the most precise classification for the quadratic form? O A. Positive semidefinite OB. Negative semidefinite OC. Positive definite OD. Indefinite O E. Negative definite The new quadratic form is y¹ 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. 8x₁ +8x₂ 2 + 8x4² + 16x₁x₂ + 16×3×4 +30x₁x4-30x2x3 +8x3 What is the most precise classification for the quadratic form? O A. Positive semidefinite OB. Negative semidefinite OC. Positive definite OD. Indefinite O E. Negative definite The new quadratic form is y¹ Dy = .

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 term. Write the new quadratic form. 2 2 8x₁² + 8x₂² +8x3² + 8x4² + 16x₁x2 + 16x3 x4 +30x₁x4-30x2x3 What is the most precise classification for the quadratic form? O A. Positive semidefinite OB. Negative semidefinite O C. Positive definite OD. Indefinite OE. Negative definite The new quadratic form is y' Dy=
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 8x₁² + 8x₂² +8x3² + 8x4² + 16x₁x2 + 16x3 x4 +30x₁x4-30x2x3 What is the most precise classification for the quadratic form? O A. Positive semidefinite OB. Negative semidefinite O C. Positive definite OD. Indefinite OE. Negative definite The new quadratic form is y' Dy=
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