Theorem FS provides the matrix
\begin{equation*}
L=
\begin{bmatrix}
\leading{1} & \frac{1}{2} & \frac{1}{4} & \frac{1}{8} & \frac{1}{16}
\end{bmatrix}
\end{equation*}
and so if $A$ denotes the coefficient matrix of the system, then $\csp{A}=\nsp{L}$. The single homogeneous equation in $\homosystem{L}$ is equivalent to the condition on the vector of constants (use $a,\,b,\,c,\,d,\,e$ as variables and then multiply by 16).