4. Consider the following matrix: 3. -2 A =-14 15 18 -18 -10 (a) Find the eigenvalues of A. (b) Find three linearly independent eigenvectors for A and state the algebraic and geometric multiplicity for each eigenvalue. Form a matrix C whose columns are the three linearly independent eigenvectors that you found in (b). Verify that C-1 AC is a diagonal matrix (which we call D). (d) Use your previous answer to find a matrix B with the property that B3 = A. (e) For any real matrix A, write down a sufficient condition for a real matrix E to exist such that E2 = A, and prove that this condition is sufficient. %3D

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