Eigenvalues, Eigenvectors and Applications: Question # 2: Part: b:Diagonalize the following matrix if possible whose eigenvalues are given to be 0, 1, 1. -1 -3 2 1 -1 0 Using this diagonalization, write three matrices product in its simplest form for A¹0. Is it same for any power Akfor this special matrix A. 0 1 A

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Application of Linear Algebra.

Eigenvalues, Eigenvectors and Applications:
Question # 2:
Part: b:Diagonalize the following matrix if possible whose eigenvalues are given to be 0, 1,
1.
-1
-1
A = 1
2
1
-1
Using this diagonalization, write three matrices product in its simplest form for Al0. Is it
same for any power Akfor this special matrix A.
Transcribed Image Text:Eigenvalues, Eigenvectors and Applications: Question # 2: Part: b:Diagonalize the following matrix if possible whose eigenvalues are given to be 0, 1, 1. -1 -1 A = 1 2 1 -1 Using this diagonalization, write three matrices product in its simplest form for Al0. Is it same for any power Akfor this special matrix A.
Linear Transformation and Applications:
Question # 3:
Part: b:Let T from R? to R? be a linear transformation that maps en into yı and maps e, into
y2 where
e2=
yı
Find the image of any x = in R2under T.
Find the standard matrix of T?
Find the range of T?
Transcribed Image Text:Linear Transformation and Applications: Question # 3: Part: b:Let T from R? to R? be a linear transformation that maps en into yı and maps e, into y2 where e2= yı Find the image of any x = in R2under T. Find the standard matrix of T? Find the range of T?
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