Create a matrix with a specific correlation within a specific distribution

I am creating matrices of random variables within the normal, uniform, and chi square distributions. However, I need to be able to specify the correlation value of the matrices.

rowsize = 10;
columnsize = 3;
dg = 2;
correlation_value = 0.7;

matrix = zeros(rowsize, columnsize);
for row = 1:rowsize
    for column = 1:columnsize
        matrix(row, column) = chi2rnd(dg);
    end
end

correlatedMatrix = SomeFunction(matrix, correlation_value);

result = corr(correlatedMatrix)

result =
    1.0000    0.7000    0.7000
    0.7000    1.0000    0.7000
    0.7000    0.7000    1.0000
    

Is there a function or some code to replace

    correlatedMatrix = SomeFunction(...)

or a function or code to replace the call to chi2rnd(dg) where result will still be within the chi square distribution?