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Chapter 7: Q39E (page 358)

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

T(f)=f'-ffromC鈭�toC鈭�

Short Answer

Expert verified

The eigenvalues and eigenvectors of the linear transformation is

位鈭�R,E位=span(e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�,herex鈫� is eigenvector andis the eigenvalue.

02

Use the formula and find the eigenvalues and eigenvectors

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

Solve,

Tf=位蹿

Substitute the value of T (f)

f'-f=位ff'=位+1ff(x)=C.e位+1x,C鈭�R

Hence, for the eigenvalue 位鈭�R, the eigenvector space isE位=span(e位+1x)

Thus,位鈭�R,role="math" localid="1659594434785" E位=spane位+1t

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Most popular questions from this chapter

For each of the matrices in Exercises 1 through 13, find all real eigenvalues, with their algebraic multiplicities. Show your work. Do not use technology.

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26: Based on your answers in Exercises 24 and 25, sketch a phase portrait of the dynamical system

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if A is a 2脳2matrix with t r A = 5and det A = - 14what are the eigenvalues of A?

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