Question: 200 a) For the given matrix A = 0 8 1 081 i) Derive a characteristic polynomial. (20 marks) ii) Find all eigenvalues and

200 a) For the given matrix A = 0 8 1 081

200 a) For the given matrix A = 0 8 1 081 i) Derive a characteristic polynomial. (20 marks) ii) Find all eigenvalues and present them in the ascending order. (30 marks) 1 5 b) For the given matrix B = i) Find the eigenvalues of B. (10 marks) ii) Find the corresponding eigenvectors. (20 marks) iii) Write the criteria for orthogonality of two eigenvectors and check whether the vectors found in part (ii) are orthogonal or not? (20 marks)

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