Question: 3. Find the eigenvalues and bases of the corresponding eigenspaces of matrix 5 3 9 A : 2 2 3 4 2 7 Hint: the

3. Find the eigenvalues and bases of the corresponding eigenspaces of matrix 5 3 9 A : 2 2 3 4 2 7 Hint: the characteristic polynomial of A is 300) = (A 1)2(/\\ 2) 4. Consider matrices 1 1 0 1 2 9 1 1/3 1/2 A: 0 3 9 A2: 0 9 31 Al: 0 1/3 1/2 0 0 6 0 0 36 0 0 1/6 (a) Find the eigenvalues of A, A2, A'l. (b) Show that eigenvectors of A are also eigenvectors for A2 and A'l

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