A change of variable, x = Py, is made to transform the original quadratic form into one with no cross product. The new quadratic form is given below. Q(Py) = 11y + 6y/2 If the eigenvectors of the original matrix are as follows: V1 = D= 1₁ Find the matrices P and D such that A P= v2 = = PDPT
A change of variable, x = Py, is made to transform the original quadratic form into one with no cross product. The new quadratic form is given below. Q(Py) = 11y + 6y/2 If the eigenvectors of the original matrix are as follows: V1 = D= 1₁ Find the matrices P and D such that A P= v2 = = PDPT
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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Question
![A change of variable, x = Py, is made to transform the original quadratic form into one with no cross product. The new quadratic form is given below.
Q(Py) = 11y1 + 6y²2
If the eigenvectors of the original matrix are as follows:
[1]
2
Find the matrices P and D such that A = PDPT
V₁ =
D=
P=
V2 =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8b609ed5-0879-4e23-8eee-4515e84ef2b9%2F469f3e4b-7bb0-4870-97e6-4f4b67f9813e%2F2zs0t1a_processed.png&w=3840&q=75)
Transcribed Image Text:A change of variable, x = Py, is made to transform the original quadratic form into one with no cross product. The new quadratic form is given below.
Q(Py) = 11y1 + 6y²2
If the eigenvectors of the original matrix are as follows:
[1]
2
Find the matrices P and D such that A = PDPT
V₁ =
D=
P=
V2 =
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P =
0 | 1 |
1 | 0 |
and D =
6 | 0 |
0 | 11 |
do not seem to be the correct answers, may there be a mistake somewhere? I went through by myself and got a similar answer, but it was also deemed incorrect. Just a bit confused.
Solution
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