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Linear Algebra With Applications
Found in: Page 442
Linear Algebra With Applications

Linear Algebra With Applications

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 λR, Eλ = spaneλ+1t.

See the step by step solution

Step by Step Solution

Step 1: Define eigenvalues

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

Ax=λx, here x is eigenvector and λ is the eigenvalue.

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

Consider the given equation, Tf=f'-f



Substitute the value of Tf=λf

f'-f=λf f'=λ+1ffx=C·eλ+1x,C R

Hence, for the eigenvalue λ R , the eigenvector space is Eλ=spaneλ+1x

Thus, λ R, Eλ=spaneλ+1t

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