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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.

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Solution Summary

The solution provides a proof regarding eigenvectors and matrices.

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 ...

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