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Question: 6 eigenvaluesvectors 366 5 20 pts a consider the matrix...

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6 Eigenvalues/vectors ((3+6+6) 5 20 pts) (a) Consider the matrix 2 12 1 2-2 (i) Show that -3 and 3 are its eigenvalues (ii) Find its eigenvectors corresponding to these eigenvalues (iii) Is it diagonalizable? If so, find a diagonalizer. (b) By using the definition of matrix exponential, find e4 where 0 1 0 A-0 0 1.

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