Find the matrix A of the quadratic form associated with the equation. 27x2 - 72xy + 48y2 – 80x – 80y + 80 = 0 27 -36 A = -36 48 Find the eigenvalues of A. (Enter your answers as a comma-separated list.) 1 =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 =
Find the matrix A of the quadratic form associated with the equation. 27x2 - 72xy + 48y2 – 80x – 80y + 80 = 0 27 -36 A = -36 48 Find the eigenvalues of A. (Enter your answers as a comma-separated list.) 1 =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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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
A =
-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.)
P =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2abc661b-c0c9-4b79-9347-0fc323cf483e%2Fbd66db5e-c63e-4ec7-8630-04ca2b9cfcba%2Fsmfwgbt_processed.png&w=3840&q=75)
Transcribed Image Text:Find the matrix A of the quadratic form associated with the equation.
27x2 - 72xy + 48y2 – 80x – 80y + 80 = 0
27
-36
A =
-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.)
P =
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