Question: (1) Consider the following two matrices and answer the subsequent questions. B = -10-1 6 -1-6 -4 -1 0 8 2 2 0 C=00-2

(1) Consider the following two matrices and answer the subsequent questions. B = -10-1 6 -1-6 -4 -1 0 8 2 2 0 C=00-2 0 0 0 (a) Compute (3 points) and factor (1 point) the characteristic polynomial of each matrix (4+4 points in total). (b) Find the eigenvalues of each matrix (2+2 points). = (c) For each matrix compute the eigenvectors associated with each eigenvalue. (d) Is the matrix B diagonalisable? Give an answer (1 point). If it is, find a diagonal matrix DB (1 point) and a matrix PB (1 point) so that DB PBPB. If it is not, provide a justification (2 points). (The part has a total value of 3 points). (e) Is the matrix C diagonalisable? Give an answer (1 point). If it is, find a diagonal matrix Dc (1 point) and a matrix Pc (1 point) so that Dc = PCPC. If it is not, provide a justification (2 points). (The part has a total value of 3 points). 8+4+10+3+3=28 marks

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