sider the following quadratic form on R²:
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: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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