I will be using this post here as a reference: How to compute the pade approximation?
After getting to the point where you solve a system of linear equations:
$$p_0 = a_0q_0\\p_1 = a_1q_0+a_0q_1\\ \ldots \\p_m = a_mq_0+a_{m-1}q_1+ \,\ldots +a_{m-n}q_n\\a_{m+1}q_0+a_mq_1+ \, \ldots a_{m-n+1}q_n = 0\\a_{m+2}q_0+a_{m+1}q_1+ \, \ldots a_{m-n+2}q_n = 0\\ \ldots \\a_{m+n}q_0+a_{m+n-1}q_1+ \, \ldots a_{m}q_n = 0$$
Sometimes the linear system of equations is represented by a matrix that is Singular (or the equations above have no solution). What does one do to make a Pade approximation work when the matrix above is singular?