# Find the eigenvalues and eigenlines of the following matrix

(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.

(i) (3,−2)

(ii) (3, 2)

Solution

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