Question: Let A be a 2 x 2 matrix with eigenvalues 4 and - and corresponding eigenvectors v, = and v2 = . Let 4Xk be

Let A be a 2 x 2 matrix with eigenvalues 4 and - and corresponding eigenvectors v, = and v2 = . Let 4Xk be a solution of the difference equation XK +1 = AXk, XO 121 a. Compute x1 = Axo. [Hint: You do not need to know A itself.] b. Find a formula for xx involving k and the eigenvectors v, and v2

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