Find the matrix A of the quadratic form associated with the equation. 4x2 - 6xy – 4y2 + 14 = 0 A = |-4 Find the eigenvalues of A. (Enter your answers as a comma-separated list.) 2 = -5,5 Find an orthogonal matrix P such that PTAP is diagonal. (Enter the matrix in the form [[row 1], [row 2], ...], where each row is a comma-separated list.) P = Need Help? Read It

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.CM: Cumulative Review
Problem 29CM
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Find the matrix A of the quadratic form associated with the equation.
4x2 - 6xy - 4y2 + 14 = 0
-3
A =
-4
Find the eigenvalues of A. (Enter your answers as a comma-separated list.)
2 = -5,5
Find an orthogonal matrix P such that PTẠP is diagonal. (Enter the matrix in the form [[row 1], [row 2], ...], where each row is a comma-separated list.)
P =
Need Help?
Read It
Transcribed Image Text:Find the matrix A of the quadratic form associated with the equation. 4x2 - 6xy - 4y2 + 14 = 0 -3 A = -4 Find the eigenvalues of A. (Enter your answers as a comma-separated list.) 2 = -5,5 Find an orthogonal matrix P such that PTẠP is diagonal. (Enter the matrix in the form [[row 1], [row 2], ...], where each row is a comma-separated list.) P = Need Help? Read It
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