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Chapter 9: Q8E (page 442)

Find all the eigenvalues and 鈥渆igenvectors鈥� of the linear transformations.

T(f)=f'鈥�ffromC''toC''

Short Answer

Expert verified

The eigenvalues and eigenvectors of the linear transformation is 位鈭�R,E位=spane位+1t.

Step by step solution

01

Define eigenvalues

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

Ax鈫�=位x鈫�, here x鈫�is eigenvector and 位is the eigenvalue.

02

Use the formula and find the eigenvalues and eigenvectors

Consider the given equation,Tf=f'-f

Solve,

Tf=位蹿

Substitute the value ofTf=位蹿

f'-f=位蹿f'=位+1ffx=C路e位+1x,C鈭�R

Hence, for the eigenvalue 位鈭�R, the eigenvector space isE位=spane位+1x

Thus,位鈭�R,E位=spane位+1t

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