# Eigenvectors and eigenvalues

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? Let . Compute the characteristic polynomial and all eigenvalues and all eigenvectors of A.

? True or false? Justify your answer in each case (giving a proof or a counterexample);

Let be a linear transformation which is an isomorphism. Denote its inverse by . Suppose that is an eigenvalue of T. then

a)

b) is an eigenvalue of .

c) - is an eigenvalue of

d) is an eigenvalue of .

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##### Solution Summary

This shows how to compute the characteristic polynomial and all eigenvalues and all eigenvectors, and show that given values are the eigenvalues of an inverse transformation matrix.

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