Question: Given matrix: (a) (b) () 2 0 1 A=|-1 a -1 -1 2 0 Find all value (s) of a such that A has eigenvalues

Given matrix: (a) (b) () 2 0 1 A=|-1 a -1

Given matrix: (a) (b) () 2 0 1 A=|-1 a -1 -1 2 0 Find all value (s) of a such that A has eigenvalues 1,2 and 3. (8 marks) Compute the eigenvectors of the corresponding eigenvalues and obtain the eigen decomposition of A. Show with working. (16 marks) Without the calculation of A! and A2, find the eigenvalues of A! and A2 (6 marks)

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