Find the matrix A of the quadratic form associated with the equation. 27x2 – 72xy + 48y2 – 80x – 80y + 80 = 0 27 A = -36 -36 48 Find the eigenvalues of A. (Enter your answers as a comma-separated list.) 2 = 0,75 Find an orthogonal matrix P such that P'AP is diagonal. (Enter the matrix in the form [[row 1], [row 2], ...], where each row is a comma-separated list.) -[[], P =

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Find the matrix A of the quadratic form associated with the equation.
27x2 - 72xy + 48y² – 80x – 80y + 80 = 0
27
|-36
-36
48
Find the eigenvalues of A. (Enter your answers as a comma-separated list.)
0,75
Find an orthogonal matrix P such that P'AP is diagonal. (Enter the matrix in the form [[row 1], [row 2], ...], where each row is a comma-separated list.)
[
4
,1
3
,1
P =
Transcribed Image Text:Find the matrix A of the quadratic form associated with the equation. 27x2 - 72xy + 48y² – 80x – 80y + 80 = 0 27 |-36 -36 48 Find the eigenvalues of A. (Enter your answers as a comma-separated list.) 0,75 Find an orthogonal matrix P such that P'AP is diagonal. (Enter the matrix in the form [[row 1], [row 2], ...], where each row is a comma-separated list.) [ 4 ,1 3 ,1 P =
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