Consider the following quadratic form on R²:- 4608x₁² + 2/2/²2 29-X11717Q(x):=b)x₁2a) Determine whether Q is positive or negative (semi)definite.b) Find a change of variables x = Py that converts Q to a form with no cross-product terms.and y2.c) write Q in terms of the new variables y1In your formula, write 'y_1' and 'y_2' for y₁ and y2. Use the square root symbol '√' where needed togive an exact value for your answer.y10012+400/Xx1a) The quadratic form is < Select an answerSelect an answer >c) Q(x) = 0-x₂² +--x1x217Positive DefiniteNegative DefinitePositive SemidefiniteNegative SemidefiniteIndefinite

Given the quadratic form on R2: Q(x)=-4617x12+2917x22+4017x1x2

Answered: sider the following quadratic form on…

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sider the following quadratic form on R²:

Elementary Algebra

17th Edition

ISBN:9780998625713

Author:Lynn Marecek, MaryAnne Anthony-Smith

Publisher:Lynn Marecek, MaryAnne Anthony-Smith

Chapter10: Quadratic Equations

Section: Chapter Questions

Problem 332PT: Use the discriminant to determine the number of solutions of each quadratic equation. 332....

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Question

Consider the following quadratic form on R²:
- 4608x₁² + 2/2/²
2 29
-X1
17
17
Q(x):
=
b)
x₁
2
a) Determine whether Q is positive or negative (semi)definite.
b) Find a change of variables x = Py that converts Q to a form with no cross-product terms.
and y2.
c) write Q in terms of the new variables y1
In your formula, write 'y_1' and 'y_2' for y₁ and y2. Use the square root symbol '√' where needed to
give an exact value for your answer.
y1
0012
+400/Xx1
a) The quadratic form is < Select an answer
Select an answer >
c) Q(x) = 0
-x₂² +-
-x1x2
17
Positive Definite
Negative Definite
Positive Semidefinite
Negative Semidefinite
Indefinite

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