Please see the attached file for full problem description.
? 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
b) is an eigenvalue of .
c) - is an eigenvalue of
d) is an eigenvalue of .
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.