5. (20 points) Let R be the recurrence relation f(n) = 7f(n-1)-16f(n-2) + 12f(n- 3) +...

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5. (20 points) Let R be the recurrence relation f(n) = 7f(n-1)-16f(n-2) + 12f(n- 3) + 14" with f(0) = -2, f(1) = 0, and f(2)= 5. (a)(2 points) What is the degree of this recurrence relation? (b)(3 points) What is the characteristic equation of R? Find the solutions of the characteristic equation (characteristic roots). (c)(3 points) What is the general form of the solution of the homogeneous part of R? (d) (2 points) What is the general form of the particular solution (the solution of the nonhomogeneous part) of R? (c)(10 points) Find all solutions of R. I 5. (20 points) Let R be the recurrence relation f(n) = 7f(n-1)-16f(n-2) + 12f(n- 3) + 14" with f(0) = -2, f(1) = 0, and f(2)= 5. (a)(2 points) What is the degree of this recurrence relation? (b)(3 points) What is the characteristic equation of R? Find the solutions of the characteristic equation (characteristic roots). (c)(3 points) What is the general form of the solution of the homogeneous part of R? (d) (2 points) What is the general form of the particular solution (the solution of the nonhomogeneous part) of R? (c)(10 points) Find all solutions of R. I