(a) Find the eigenvalues and eigenlines of the following matrix A. For each eigenvalue, give an eigenvector with integer components.
A = ( 5 3 ) -top
(−6 −6 ) - bottom
(b) Express the matrix A in the form PDP^−1, where D is a diagonal
matrix. You should evaluate P and P^−1.
(c) Use part (b) to find the matrix A^6.
(d) Calculate the second and third points of the iteration sequence with
recurrence relation xn+1 = Axn (n = 0,1,2, . . .), for each of the
following initial points.
(ii) (3, 2)
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