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## Homework Statement

If v is an eigenvector of A with corresponding eigenvalue [tex]\lambda[/tex] and c is a scalar, show that v is an eigenvector of A-cI with corresponding eigenvalue [tex]\lambda[/tex]-c.

## Homework Equations

## The Attempt at a Solution

I started out thinking that I have to figure out how to go from:

Ax=[tex]\lambda[/tex]x

to

(A-cI)x=([tex]\lambda[/tex]-c)x

Is this the right start?