A triangular n x n matrix A is defined by the condition A = 0 for...

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A triangular n x n matrix A is defined by the condition A¡¡ = 0 for i > j. By using a cofactor expansion of the determinant of (A-AI), demonstrate that the eigenvalues of the triangular matrix A are the entries of its main diagonal A¡¡ (1 ≤ i ≤n) Using the result demonstrated in the previous problem, demonstrate that a triangular matrix with distinct diagonal entries is diagoanlizable. A triangular n x n matrix A is defined by the condition A¡¡ = 0 for i > j. By using a cofactor expansion of the determinant of (A-AI), demonstrate that the eigenvalues of the triangular matrix A are the entries of its main diagonal A¡¡ (1 ≤ i ≤n) Using the result demonstrated in the previous problem, demonstrate that a triangular matrix with distinct diagonal entries is diagoanlizable.