Consider the following matrices A and B: 200 2 -1 A=0 1 1 B = -1...

  

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Consider the following matrices A and B: 200 2 -1 A=0 1 1 B = -1 2 0 ' 0 1 1 0 0 1 (1) For each of A and B, determine its eigenvalues and eigenspaces. (2) Find all the vectors in R which are eigenvectors of both A and B. (3) Show that the vectors found in (2) above are eigenvectors of every 3 3 matrix M such that AM = MA and BM = MB. (4) Show that every 3 3 matrix M such that AM nalizable. == MA and BM = MB is diago- Consider the following matrices A and B: 200 2 -1 A=0 1 1 B = -1 2 0 ' 0 1 1 0 0 1 (1) For each of A and B, determine its eigenvalues and eigenspaces. (2) Find all the vectors in R which are eigenvectors of both A and B. (3) Show that the vectors found in (2) above are eigenvectors of every 3 3 matrix M such that AM = MA and BM = MB. (4) Show that every 3 3 matrix M such that AM nalizable. == MA and BM = MB is diago-