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(Linear Algebra) Consider the difference equation. yk+2 - 4yk+1 + 4yk = 0, for all k...

(Linear Algebra) Consider the difference equation.

yk+2 - 4yk+1 + 4yk = 0, for all k

(a) After using auxiliary equation, the solutions have the form rk and k(rk). Find the root, r, and show that yk = k(rk) is a solution.

(b) Show that rk and k(rk) are linearly independent and form the general solution of the difference equation.

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