Book edition 5th

Author(s) Otto Bretscher

Pages 442 pages

ISBN 9780321796974

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Short Answer

Find all the eigenvalues and “eigenvectors” of the linear transformations.
$T (f) = f' ‐ f from C'' to C''$

The eigenvalues and eigenvectors of the linear transformation is $λ \in R_{,} E_{λ} = span (e^{(λ + 1) t})$ .

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Define eigenvalues

The scalar values that are associated with the vectors of the linear equations in the matrix are called eigenvalues.

$A \vec{x} = λ \vec{x}$ , here $\vec{x}$ is eigenvector and $λ$ is the eigenvalue.

Step 2: Use the formula and find the eigenvalues and eigenvectors

Consider the given equation, $T (f) = f' - f$

Solve,

$T (f) = λf$

Substitute the value of $T (f) = λf$

$f' - f = λf f' = (λ + 1) f f (x) = C \cdot e^{(λ + 1) x}, C \in R$

Hence, for the eigenvalue $λ \in R$ , the eigenvector space is $E_{λ} = span (e^{(λ + 1) x})$

Thus, $λ \in R, E_{λ} = span (e^{(λ + 1) t})$

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Linear Algebra With Applications

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Short Answer

Find all the eigenvalues and “eigenvectors” of the linear transformations.
$T (f) = f' ‐ f from C'' to C''$

Step by Step Solution

Step 1: Define eigenvalues

Step 2: Use the formula and find the eigenvalues and eigenvectors

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Linear Algebra With Applications

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Short Answer

Find all the eigenvalues and “eigenvectors” of the linear transformations.T(f)=f'‐f from C'' to C''

Step by Step Solution

Step 1: Define eigenvalues

Step 2: Use the formula and find the eigenvalues and eigenvectors

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Find all the eigenvalues and “eigenvectors” of the linear transformations.
$T (f) = f' ‐ f from C'' to C''$