Question: Algebra 5 0 -12 Let A = 0 3 0 3 0 5 (a) (2 marks) Find the characteristic polynomial of A. CA( 2 )

Algebra

5 0 -12 Let A = 0 3 0 3 0 5 (a) (2 marks) Find the characteristic polynomial of A. CA( 2 ) = (12 - -2) (All the numbers to be entered in this polynomial should be real.) (b) (3 marks) The eigenvalues of A are and (c) (3 marks) The matrix A is diagonalizable over C. Find an invertible complex 3 x 3 matrix P and a diagonal complex 3 x 3 matrix D such that PAP = D P and D =

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