IN MATLAB

Part 1: Recursive Mat Mul Your task is to create three functions for multiplying two nx nmatrices, having the following forms: 1. function C- defaultMatMul(A,B) 2. function C-myMatMul(A,B) 3. function C- recMatMul(A, B) The first just uses CA*B, using Matlab's default matrix multiplication algorithm The second uses three nested loops and the formula 10 and therefore uses only scalar multiplication as a primitive The third is a recursive algorithm, with base case when n-1 (just c-a . b), and uses the recursion 21 The function will therefore involve calling eight recursive calls, each on a problem half the size of the original: C11 recMatMul (A11,B11) + recMatMul(A12, B21) . C22 = recMatMul (A21 , B12) + recMatMul (A22, B22) You may assume for the purposes of your recursive algorithm that n is a positive integer of the form 2". Thus you can divide the matrices neatly in half at every step Part 2: Plotting Use code along the lines of tic; CODE HERE; timeElapsed toc (check the documen- tation on tic and toc) to record the time required for matrix multiplication by each algo- rithm. Use A randn(n,n) ; B randn(n,n) to make random n n matrices and time how long it takes each of your algorithms to compute C-AB for n 32, 64,128,... , 4096 (or 8192, if your computer can handle it). Make a plot with one line for each method. If you want to get clearer results you may optionally run each trial multiple times and report the average