I have the following
m=5; n=3
A = matrix(QQ, (m^n)^2+1, (m^m)^2)
A[0, :] = ones_matrix(1, (m^m)^2)
for i in [1..(m^n)^2]: A[i,(m^(2*(m-n)))*(i-1):(m^(2*(m-n)))*i] = ones_matrix(1, m^(2*(m-n)))
E = A.right_kernel()
And I get the message: the kernel died... Any suggestion to big matrices?