How can I produce this matrix?

I want to produce a m×n (m<n) matrix in which each element can only be 0 or 1 and the sum of first row must be n-(m-1) and the sum of each column must be 1. For example it can be similar to this: [1 1 0 0 1 1; 0 0 0 1 0 0; 0 0 1 0 0 0]

Answer 1

[Bruno Luong]

m=6

m = 6

n=3

n = 3

j=randperm(m,n-1);
A=accumarray([2:n;j]',1,[n,m]);
A(1,setdiff(1:end,j))=1

A = 3×6

1 0 1 1 1 0 0 1 0 0 0 0 0 0 0 0 0 1

[S AsZ]

Thank you 🙏🏻