1. Consider multiplication of two matrices A and B. each of size nxn. Let the product be matrix C = A x B. Suppose n = 2 for some integer k. Consider the classical matrix multiplication algorithm implemented using a divide-and-conquer approach. Each matrix is divided into 4 quadrants, each of size n/2xn/2. Then matrix multiplication is carried out as if all quadrants were single elements. C CH [CC] - [AA] [BB (a) Write down the expression for each of the quadrants in the product matrix C. (The expression for C is already provided.) C = A x B+ A2 x B1 (b) Let T(n) be the total number of simple arithmetic operations (ie., number of mutiplica- tions and additions) for this divide-and-conquer algorithm to multiply two nxn matrices. Write a recurrence equation for T(n). Provide a brief explanation for each term. (e) Use Master-Theorem to obtain the solution.