Question: Let A denote an n Ã n upper triangular matrix. (a) If all the main diagonal entries of A are distinct, show that A is

Let A denote an n Ã— n upper triangular matrix.
(a) If all the main diagonal entries of A are distinct, show that A is diagonalizable.
(b) if all the main diagonal entries of A are equal, show that A is diagonalizable only if it is already diagonal.
(c) Show that

Is diagonalizable but that

Is not diagonalizable.

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