Let λ ER and consider the matrix J = 1 0 X 0 0 00 1 0 0 λ 1 0 0 X € M4. (a) Show that A is the only eigenvalue of J. What is its algebraic multiplicity? (b) Find a basis for E(J, λ) and determine the geometric multiplicity of X. (c) Using your answers in (a) and (b) together with Theorem 3.32, explain why J is not diagonalizable.

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