Question: Let A = 2 0 0 2 0 1 0 1 , where is some real number. (1) Find the eigenvalues of A . (2)

Let A= 20020101, where is some real number.

(1) Find the eigenvalues of A.

(2) Find a basis and the dimension of each eigenspace of A. (Warning: your answer should depend on )

(3) Find all values of for which A has an eigenbasis and write it down. (Here, an eigenbasis is a basis of R3consisting of three linearly independent eigenvectors of A)

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