Linear Algebra with Applications 1st. Edition by Jeffrey Holt | 9780716786672 | 0716786672 | Holooly

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. ...

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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. ...

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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. ...

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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) ...

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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] ...

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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] ...

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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] ...

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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] ...

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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] ...

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We start by finding the eigenvalues of A by comput...

Question: 6.1.3

Find the eigenvalues for A =[3 3 6 -4]. ...

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Our strategy is to determine the values of λ that ...

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