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

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.1: Eigenvalues And Eigenvectors
Problem 77E
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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 =
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.

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