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I would like some detailed explanation for the following systems of equations problem (b) For the matrix A = 3 -2 12 3 5 Determine

I would like some detailed explanation for the following systems of equations problem

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(b) For the matrix A = 3 -2 12 3 5 Determine the characteristic equation and the characteristic roots. ( ii) Determine the eigenvectors. (iii) Diagonalize A. Ensure that you explain each step in the computation. (20 marks) (iv) Why is it useful to diagonalize a matrix? (1 mark)

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