# Eigenvectors

D and E are nxn matrices, E is invertible, DE = ED, and u is an eigenvector for D corresponding to x=5.

a. Show that Eu is also an eigenvector for D corresponding to x=5.

b. Show that u is an eigenvector for D^2.

c. Show that u is an eigenvector for

D^2 - 3D.

https://brainmass.com/math/linear-algebra/computing-proof-regarding-eigenvectors-matrices-1563

#### Solution Preview

See the attached file.

a) We know:

Du=5u (u is eigenvector for 5) and DE=ED(*). Let's multiply the first equality by E to the left.

Then, EDu=5Eu so DEu=5Eu because of ...

#### Solution Summary

The solution provides a proof regarding eigenvectors and matrices.

$2.19