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Linear Algebra
Linear Algebra with Applications
282 SOLVED PROBLEMS
Question: 6.2.4
For the matrix A given in Example 1, find the eigenvalue that is closest to c = 4. ...
Verified Answer:
We start by setting
B=A-4 I_5=\left[\begin{...
Question: 6.2.3
For the matrix A in Example 1, find the smallest eigenvalue (in absolute value) and an associated eigenvector. ...
Verified Answer:
Here we apply the Power Method to
A^{-1}=\f...
Question: 6.2.2
For the matrix A given in Example 1, find the eigenvalue (and an associated eigenvector) farthest from λ1 = 13. ...
Verified Answer:
To find λ
_2
, the eigenvalue of A fa...
Question: 6.2.1
Find an eigenvector and associated eigenvalue for the matrix A =[245 -254 -252 -46 -224 161 -168 -174 -32 -148 -39 40 45 7 38 27 -28 -32 -6 -26 110 -113 -110 -21 -101](3) ...
Verified Answer:
We apply the Power Method starting with x
_0...
Question: 6.1.8
Show that λ = 0 is an eigenvalue for the matrix A =[3 -1 5 2 1 0 4 1 2] ...
Verified Answer:
From the Big Theorem, Version 8, λ = 0 is an eigen...
Question: 6.1.7
Find the eigenvalues and a basis for each eigenspace of A =[0 2 -1 1 -1 0 1 -2 0] ...
Verified Answer:
The characteristic polynomial of A is
\oper...
Question: 6.1.6
Find the eigenvalues and a basis for each eigenspace of A =[1 -2 1 -1 0 1 -1 -2 3] ...
Verified Answer:
We start out by finding the eigenvalues for A by c...
Question: 6.1.5
Find the eigenvalues and a basis for each eigenspace of A =[1 -3 3 2 -2 2 2 0 0] ...
Verified Answer:
We determine the eigenvalues of A by calculating t...
Question: 6.1.4
Find the eigenvalues and a basis for each eigenspace for the matrix A = [2 -1 -1 2] ...
Verified Answer:
We start by finding the eigenvalues of A by comput...
Question: 6.1.3
Find the eigenvalues for A =[3 3 6 -4]. ...
Verified Answer:
Our strategy is to determine the values of λ that ...
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