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 2 +8X3 2 +8X4 + A. Indefinite B. Negative semidefinite C. Positive definite D. Negative definite E. Positive semidefinite 16x₁x₂ + 16x3x4 - 30x₁x4 +30×₂×3 What is the most precise classification for the quadratic form? T The new quadratic form is y¹ Dy = 9y₁2 2 +9y2 2-25Y4 2 - 25y3
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 2 +8X3 2 +8X4 + A. Indefinite B. Negative semidefinite C. Positive definite D. Negative definite E. Positive semidefinite 16x₁x₂ + 16x3x4 - 30x₁x4 +30×₂×3 What is the most precise classification for the quadratic form? T The new quadratic form is y¹ Dy = 9y₁2 2 +9y2 2-25Y4 2 - 25y3
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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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
8x₁ +8x2 + +8x3² +8X4
2
2
+ 16x₁x2 + 16×3×4 - 30x₁x4 +30x₂x3
What is the most precise classification for the quadratic form?
A. Indefinite
B. Negative semidefinite
C. Positive definite
D. Negative definite
E. Positive semidefinite
T
The new quadratic form is y' Dy=
2
9y1
2-25y3
2-2514
+9y₂
2
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