Let the eigenvalues of the matrix A be 11, A2, . . An and the linearly ww w wwwww www independent eigenvectors corresponding to these eigenvalues V1,V2,..., Vn . (S [V¡V2 . . Vn]nxn) by placing the vectors V1,V2,..., Vn in each column of A is the eigenvalue of V1,V2,..., Vn placed on the wwww the S matrix; If the matrix wmwm w m ww. diagonal, prove that, diagonal matrix. Also show that eAt = A = SAS-1 (A diag[A1 ^2 . ..An]nxn) with in the w ww uwww SeAt s-1 ww w w w w w e
Let the eigenvalues of the matrix A be 11, A2, . . An and the linearly ww w wwwww www independent eigenvectors corresponding to these eigenvalues V1,V2,..., Vn . (S [V¡V2 . . Vn]nxn) by placing the vectors V1,V2,..., Vn in each column of A is the eigenvalue of V1,V2,..., Vn placed on the wwww the S matrix; If the matrix wmwm w m ww. diagonal, prove that, diagonal matrix. Also show that eAt = A = SAS-1 (A diag[A1 ^2 . ..An]nxn) with in the w ww uwww SeAt s-1 ww w w w w w e
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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![Let the eigenvalues of the matrix A be
A1, A2, . . A,n and the linearly
w m w w w
w w ma
ndependent eigenvectors corresponding to these eigenvalues V1,V2,.. Vn.
....
ww m ww
(S
[V1V2 . .. Vn]nxn)
||
by placing the vectors V1,V2,., Vn in each column of
A is the eigenvalue of V1,V2,.., Vn placed on the
w w m
w m w w
the S matrix; If the matrix
diagonal, prove that,
diagonal matrix. Also show that eAt
mw wm m m
w
ww
diag[A1 A2 . .. A,]nxn) with in the
A
= SAS-1
(A
SeAt s-1 .
%3D
ww w w w w m](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2261ac73-d86a-4af1-9372-4cef84be1b56%2Fd6d8e079-dab1-411b-92df-1b3195c6b4c6%2Fetmyfsk_processed.png&w=3840&q=75)
Transcribed Image Text:Let the eigenvalues of the matrix A be
A1, A2, . . A,n and the linearly
w m w w w
w w ma
ndependent eigenvectors corresponding to these eigenvalues V1,V2,.. Vn.
....
ww m ww
(S
[V1V2 . .. Vn]nxn)
||
by placing the vectors V1,V2,., Vn in each column of
A is the eigenvalue of V1,V2,.., Vn placed on the
w w m
w m w w
the S matrix; If the matrix
diagonal, prove that,
diagonal matrix. Also show that eAt
mw wm m m
w
ww
diag[A1 A2 . .. A,]nxn) with in the
A
= SAS-1
(A
SeAt s-1 .
%3D
ww w w w w m
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