Question: Questions 1-2-3 1. Find the characteristic polynomial, the eigenvalues, and the associated eigenspaces for the following matrix: 2 0 -1 4 0 3 2 2.

Questions 1-2-3

1. Find the characteristic polynomial, the eigenvalues, and the associated eigenspaces for the following matrix: 2 0 -1 4 0 3 2 2. Find a basis for the eigenspace associated with eigenvalue ^ = 3 for the following matrix: 3 0 0 -2 -2 2 0 5 3. Find the eigenvalues and eigenvectors of A and of A + I where 1 4 A = 2 3 You should find that the eigenvectors are the same. Is this true in general? Why or why not? How are the eigenvalues of A + I in related to the eigenvalues of A

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