1.2 More Efficient Calculation In the class we talked about two algorithms for calculating Fn. We find another algorithm that is even faster than the previous ones. This new algorithm involves matrix multiplication. Let us start with the following observation. [F1F2]=[0111][F0F1] Similarly we have [F2F3]=[0111][F1F2]=[0111]2[F0F1] and in general [FnFn+1]=[0111]n[F0F1]. Let's denote X=[0111]. Building on our observation, to calculate Fn it suffices to calculate Xn and do a simple matrix multiplication. (a) Show that two 22 matrices can be multiplied using 4 additions and 8 multiplications. (b) Show that O(logn) matrix multiplications suffice for computing Xn. (Hint: first calculate X2n.) (c) Explain why the time-complexity of this algorithm is not O(logn). (Hint: multiplying big numbers is not free.)