3. Compare performances of different implementations of the matrix-vector multiplication. An incomplete Matlab code matvecprod.m is attached. (a) Complete the code for matrix-vector multiplication. (b) Run the program on your computer and record the time needed for each implementation. Here are two remarks. 1. Different implementations may have very different performances, though mathematically they are equivalent. 2. We should call build-in functions for matrix computations if they are available, because they are optimized for your computer. n=10000; A=rand(n); b=rand(n,1); c=zeros(n,1); %%% The following is the first implementation of c=A*b using ij - loop. tic; for i=1:n for j=1:n % complete the missing line to update c(i) end end disp(['ij loop, time: ' num2str(toc) 1 seconds']); %%% The following is the second implementation of c=A*b using ji-loop. c=zeros(n,1); tic; for j=1:n for i=1:n % complete the missing line to update c(i) end end disp(['ji loop, time: num2str(toc) seconds']); %%% The following is the last implementation of c=A*b by calling the build-in function. tic; C=A*b; disp(['build-in function, time: num2str(toc) seconds']); 1