Consider the following quadratic form on R²: Q(x) = ²x₂²¹ +27x₂² +48x2x2 43 2 57 -x1 25 25 25 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. c) write Q in terms of the new variables y/1 and 1/2- In your formula, write 'y_1' and 'y_2' for 1₁ and 12. Use the square root symbol '√' where needed to give an exact value for your answer. a) The quadratic form is < Select an answer > < Select an answer > Positive Definite Negative Definite Positive Semidefinite Negative Semidefinite Indefinite [001] 004₂ b) - c) Q(x) = 0
Consider the following quadratic form on R²: Q(x) = ²x₂²¹ +27x₂² +48x2x2 43 2 57 -x1 25 25 25 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. c) write Q in terms of the new variables y/1 and 1/2- In your formula, write 'y_1' and 'y_2' for 1₁ and 12. Use the square root symbol '√' where needed to give an exact value for your answer. a) The quadratic form is < Select an answer > < Select an answer > Positive Definite Negative Definite Positive Semidefinite Negative Semidefinite Indefinite [001] 004₂ b) - c) Q(x) = 0
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![Consider the following quadratic form on R²:
43 2 57 2
+
-x7²
25
-X₂
2
25
Q(x)
=
[₁]
=
48
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.
c) write Q in terms of the new variables y 1 and y2.
In your formula, write 'y_1' and 'y_2' for y₁ and y2. Use the square root symbol 'V' where needed to give an exact value for
your answer.
[00₁]
0 0 1
00 42
+.
a) The quadratic form is < Select an answer >
< Select an answer >
c) Q(x) = 0
25
-X1X2
Positive Definite
Negative Definite
Positive Semidefinite
Negative Semidefinite
Indefinite](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F373110e7-e385-4127-adf5-b0ae0e197db9%2Ffd21a2da-45cd-47f2-a552-1deee1b38305%2F8upbdih_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the following quadratic form on R²:
43 2 57 2
+
-x7²
25
-X₂
2
25
Q(x)
=
[₁]
=
48
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.
c) write Q in terms of the new variables y 1 and y2.
In your formula, write 'y_1' and 'y_2' for y₁ and y2. Use the square root symbol 'V' where needed to give an exact value for
your answer.
[00₁]
0 0 1
00 42
+.
a) The quadratic form is < Select an answer >
< Select an answer >
c) Q(x) = 0
25
-X1X2
Positive Definite
Negative Definite
Positive Semidefinite
Negative Semidefinite
Indefinite
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