Writing a code with the size of the (square) matrix increasing in dimensions

I'm trying to write a code to solve for shift factors. The problem I'm having is that what I need will require the code to solve for 2 variables then 3 then 4 but without the previous variables changing. I need a general code that will first solve 2 variables (2x2 matrix) then 3 variables with the first 2 the same (3x3 matrix) then 4 variables with the first 3 the same (4x4 matrix) and so on. How would I solve for this where the size of the matrix increases and the previously solved variables remain constants?

Here's what I have so far but I need a loop of some sort to make it general.

    SP = xlsread('Shift Factor Data',-1);
    SPj = SP(1:end);
    MCC = xlsread('Shift Factor Data',-1);
    MCCj = MCC(1:end);
    A = [SPj(1,1) M(1,1); SPj(1,1) SPj(2,1)];
    B = [-MCCj(1,1); -MCCj(2,1)];
    Shift_Factor = A\B
    C = [SPj(1,1) 0 0; SPj(1,1) SPj(2,1) 0; SPj(1,1) SPj(2,1) SPj(3,1)];
    D = [-MCCj(1,1); -MCCj(2,1); -MCCj(3,1)];
    SF = C\D