Solve the following recurrence relation with the method of the charac- teristic equation: T(n) 4T (n/2)+(n/2), for n > 1, n a power of 2 T(1)=1 Determine the coefficients. (b) (1 PT.) What is the (big O) order of the solution as a function of n? (c) (5 PTS.) Verify your solution by substituting back in the recurrence relation. (ii) (10 PTS.) Solve using the method of the characteristic equation to find the (big O) order of T(n) if n is a power of 3 and if T(n) 4T(n/3)+n(n-1) log, n, for n > 1