-1 2 020 2and an orthogonal matrixGiven a symmetric matrix A%3D2 112P = -2 2that diagonalizes A to D = PT AP = PAP" = diag(A3, A2, A1) where%3D1%3D2 -21, 12, Az are the eigenvalues of A corresponding to the eigenvectors V1, V2, V3a) Determine the eigenvalues and eigenvectors of AAs =b) If Q(x) == x' Ax where x =

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-1 2 0 Given a symmetric matrix A 2 0 2 and an orthogonal matrix 2 1 1 that diagonalizes A to D = PT AP = PAPT = diag(A3, A2, A1) where P = -2 2 1 2 -2 %3D %3D 1 1, A2, A3 are the eigenvalues of A corresponding to the eigenvectors V1, V2, V3 a) Determine the eigenvalues and eigenvectors of A As =

-1 2 0 Given a symmetric matrix A 2 0 2 and an orthogonal matrix 2 1 1 that diagonalizes A to D = PT AP = PAPT = diag(A3, A2, A1) where P = -2 2 1 2 -2 %3D %3D 1 1, A2, A3 are the eigenvalues of A corresponding to the eigenvectors V1, V2, V3 a) Determine the eigenvalues and eigenvectors of A As =

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

-1 2 0
2
0 2
and an orthogonal matrix
Given a symmetric matrix A
%3D
2 1
1
2
P = -2 2
that diagonalizes A to D = PT AP = PAP" = diag(A3, A2, A1) where
%3D
1
%3D
2 -2
1, 12, Az are the eigenvalues of A corresponding to the eigenvectors V1, V2, V3
a) Determine the eigenvalues and eigenvectors of A
As =
b) If Q(x) =
= x' Ax where x =

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