Eigenvalues and eigenvectors of a linear transform

[smithg86]

Homework Statement

Find all the eigenvalues and eigenvectors of the linear transformation:
T(f) = 5f ' -3f
T: from C^(nfnty) --> C^(nfnty)
where C^(nfnty) is set of continuously functions

Homework Equations

A scalar B is called an eigenvalue of T if there exists a nonzero element f of C such that:
T(f) = Bf

The Attempt at a Solution

didn't know where to start

 

[matt grime]

You do know where to start. You have said you need to find all functions f and a scalars, B so that

5f'-3f=Bfso find them. That part is first year calculus: first order linear homogeneous differential equation.

 

[Dick]

T(f)=Bf so 5*f'-3*f=B*f. It's an ODE. Solve it.