Help Coding Sudoku Constraints for Project

Im doing a project about solving sudokus with orthogonal matching pursuit and got stuck trying to write code for one of the constraints.

I understand that the constraint that i'm attempting to write code for should allow for all 81 of the cells to be filled with a value between 1-9. The issue is that i'm not sure how to get started with writing that particular code in matlab.

%%
A = zeros(324,729);
% Row j has one k
for j=1:9
    for k=1:9
        RowA = (j-1)*9+k;
        ColA = 81*(j-1)+(k-1)+[1:9:81];
        A(RowA,ColA) = ones(1,9);
    end
end
% Box (m,n) has one k
for j=1:9
    m = ceil(j/3);
    n = 1+mod(j-1,3);
    for k=1:9
        RowA = 81 + (j-1)*9+k;
        ColA = (m-1)*243+(n-1)*27+(k-1)+[1 10 19 82 91 100 163 172 181];
        A(RowA,ColA) = ones(1,9);
    end
end
% Col j has one k
for j=1:9
    for k=1:9
        RowA = 162 + 9*(j-1)+(k-1)+[1:9:81];
        ColA = 81*(j-1)+k;
        A(RowA,ColA) = ones(1,9);
    end
end
% Cell (m,n) has one value
%% Cell (m,n) equals given value

[per isakson]

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