Question: a. Let A be a diagonalizable n n matrix. Show that if the multiplicity of an eigenvalue is n, then A = I.

a. Let A be a diagonalizable n × n matrix. Show that if the multiplicity of an eigenvalue  λ is n, then A = λI.


b. Use part (a) to show that the matrixA = 2 1 0 0 2 1 0 0 2is not diagonalizable.

A = 2 1 0 0 2 1 0 0 2

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