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. - 2x; - 6x, - 8x - 8x + 4x,x2 + 4XqX3 + 4x,Xq + 4X3%g Classify the given quadratic form. O A. Positive semidefinite B. Negative semidefinite O C. Indefinite O D. Positive definite O E. Negative definite The new quadratic form is y' Dy = (Simplify your answer.)

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. - 2x; - 6x, - 8x - 8x + 4x,x2 + 4XqX3 + 4x,Xq + 4X3%g Classify the given quadratic form. O A. Positive semidefinite B. Negative semidefinite O C. Indefinite O D. Positive definite O E. Negative definite The new quadratic form is y' Dy = (Simplify your answer.)

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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Roots

The main dissimilarity between real and complex roots is that the real roots are obtained as real numbers, in contrast with the complex roots, which are indicated as imaginary numbers. The standard format for depicting any complex number is in the form of a + bi.

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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.
- 2x; - 6x, - 8x - 8x + 4x,x2 + 4XqX3 + 4x,Xq + 4X3%g
Classify the given quadratic form.
O A. Positive semidefinite
B. Negative semidefinite
O C. Indefinite
O D. Positive definite
O E. Negative definite
The new quadratic form is y' Dy =
(Simplify your answer.)

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