How to turn this for loop into a matrix?

My code spends a significant amount of time in for loop. Could you, please, help to convert this for loop to a matrix operation? Please, notice that each output is an input for the next step.

        b=[1x9 array]';
        y=[1x9 array]';
        expmA = zeros(100,9,9 );
  Ainvbm = zeros(100, 9); 

        for m=1:100;

        Ma = [ 1x9 array ]; contains m-dependent variable
        Mb =  [ 1x9 array ]; contains m-dependent variable
        Mc =  [ 1x9 array ]; contains m-dependent variable
        Md =  [ 1x9 array ]; contains m-dependent variable
        Me = [ 1x9 array ]; contains m-dependent variable
        Mf = [ 1x9 array ]; contains m-dependent variable
        Mg =  [ 1x9 array ]; contains m-dependent variable
        Mh =  [ 1x9 array ]; contains m-dependent variable
        Mj =  [ 1x9 array ]; contains m-dependent variable

        A = [Ma; Mb; Mc; Md; Me; Mf; Mg; Mh; Mj];

        expmA(m,:,:)= expm(A*time(m));
  Ainvbm(m,:) = A\b;
        end

% This loop is bottleneck of my code. How to convert it to a matrix operation?
            for m=1:100;
                y = squeeze(expmA(m,:,:))*(y+Ainvbm(m,:)')-Ainvbm(m,:)';
            end

[Azzi Abdelmalek]

Your question is not clear, give a short numeric example

[Alex]

I added more details to the code. Hope it is more clear now. Thank you for your time.

[Jan]

" b=[1x9 array]'" is not useful. Better post in valid Matlab syntax.

Answer 1

[Star Strider]

If [Ma ... Mj] and A don’t change in the loop, define them once before the loop rather than in each iteration of the loop.

This code ran quickly:

time = 0:0.01:0.99;
A = -rand(9,9);
b = rand(1,9)';
y = rand(1,9)';
tic
for m = 1:100
    expmA(m,:,:) = expm(A*time(m));
    Ainvbm(m,:) = A\b;
end

for m = 1:100
    y = squeeze(expmA(m,:,:))*(y+Ainvbm(m,:)')-Ainvbm(m,:)';
end
toc

Elapsed time is 0.046041 seconds.