Show that the 5 × 5 matrix
has an eigenvalue λ1 of multiplicity 5. Show that three linearly independent eigenvectors corresponding to λ1 can be found. Consider the 5 × 5 matrix given in Problem 33. Solve the system X′ = AX without the aid of matrix methods, but write the general solution using matrix notation. Use the general solution as a basis for a discussion of how the system can be solved using the matrix methods of this section. Carry out your ideas.
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