1) Consider the following two matrices and answer the subsequent questions. 1 4 -12 -1 2 0 B= -15 -15 33 C= 1 0 0 -5 -4

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1 Consider The Following Two Matrices And Answer The Subsequent Questions 1 4 12 1 2 0 B 15 15 33 C 1 0 0 5 4 1 (116.12 KiB) Viewed 37 times

1) Consider the following two matrices and answer the subsequent questions. 1 4 -12 -1 2 0 B= -15 -15 33 C= 1 0 0 -5 -4 8 [0 -2 1 (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 (2 marks for each eigenvalue) (6+6 points in total). (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 = PE+BP3. 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 = Pc-CPc. If it is not, provide a justification (2 points). (The part has a total value of 3 points).