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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 4x1 2 + 4x3 4X2 2 + 2 OA. Positive definite B. Negative definite +4x4 +8x1x2 + 8x3x4 + 6x1x4 - 6x2x3 What is the most precise classification for the quadratic form? OC. Indefinite OD. Positive semidefinite E. Negative semidefinite 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. 2 4x1 2 + 4x3 4X2 2 + 2 OA. Positive definite B. Negative definite +4x4 +8x1x2 + 8x3x4 + 6x1x4 - 6x2x3 What is the most precise classification for the quadratic form? OC. Indefinite OD. Positive semidefinite E. Negative semidefinite 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 4x1 2 2 +4x2 +4x3 2 +4x4 + 8x₁x₂ + 8×3×4 + 6×₁X4 − 6x2x3 What is the most precise classification for the quadratic form? A. Positive definite B. Negative definite C. Indefinite D. Positive semidefinite OE. Negative semidefinite Т 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 4x1 2 2 +4x2 +4x3 2 +4x4 + 8x₁x₂ + 8×3×4 + 6×₁X4 − 6x2x3 What is the most precise classification for the quadratic form? A. Positive definite B. Negative definite C. Indefinite D. Positive semidefinite OE. Negative semidefinite Т The new quadratic form is y Dy =
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