\begin{table}%t6
\caption{\label{t3}Coefficient submatrix relating the first column~$\vec{A}$ of matrix~${\bf Y}$ and the first column~$\vec{a}$ of matrix~${\bf X}$.}
$$
\left[ \begin{array}{cccccccccccccccccccc} 1&0&0&{\it m}_{{1}}&{\it m}_{{2}}&{\it m}_{{3}}&0&0&0&{\it m}_{{1 1}}&2~{\it m}_{{1 2}}&2~{\it m}_{{1 3}}&{\it m}_{{2 2}}&2~{\it m}_{{2 3}}&{\it m}_{{3 3}}&0&0&0&0&\cdots\\
\noalign{\medskip}{\it m}_{{1}}&0&0&{\it m}_{{1 1}}&{\it m}_{{1 2}}&{\it m}_{{1 3}}&0&0&0&{\it m}_{{1 1 1}}&2~{\it m}_{{1 1 2}}&2~{\it m}_{{1 1 3}}&{\it m}_{{1 2 2}}&2~{\it m}_{{1 2 3}}&{\it m}_{{1 3 3}}&0&0&0&0&\cdots\\
\noalign{\medskip}{\it m}_{{2}}&0&0&{\it m}_{{1 2}}&{\it m}_{{2 2}}&{\it m}_{{2 3}}&0&0&0&{\it m}_{{1 1 2}}&2~{\it m}_{{1 2 2}}&2~{\it m}_{{1 2 3}}&{\it m}_{{2 2 2}}&2~{\it m}_{{2 2 3}}&{\it m}_{{2 3 3}}&0&0&0&0&\cdots\\
\noalign{\medskip}{\it m}_{{3}}&0&0&{\it m}_{{1 3}}&{\it m}_{{2 3}}&{\it m}_{{3 3}}&0&0&0&{\it m}_{{1 1 3}}&2~{\it m}_{{1 2 3}}&2~{\it m}_{{1 3 3}}&{\it m}_{{2 2 3}}&2~{\it m}_{{2 3 3}}&{\it m}_{{3 3 3}}&0&0&0&0&\cdots\\
\noalign{\medskip}{\it m}_{{1 1}}&0&0&{\it m}_{{1 1 1}}&{\it m}_{{1 1 2}}&{\it m}_{{1 1 3}}&0&0&0&{\it m}_{{1 1 1 1}}&2~{\it m}_{{1 1 1 2}}&2~{\it m}_{{1 1 1 3}}&{\it m}_{{1 1 2 2}}&2~{\it m}_{{1 1 2 3}}&{\it m}_{{1 1 3 3}}&0&0&0&0&\cdots\\
\noalign{\medskip}{\it m}_{{1 2}}&0&0&{\it m}_{{1 1 2}}&{\it m}_{{1 2 2}}&{\it m}_{{1 2 3}}&0&0&0&{\it m}_{{1 1 1 2}}&2~{\it m}_{{1 1 2 2}}&2~{\it m}_{{1 1 2 3}}&{\it m}_{{1 2 2 2}}&2~{\it m}_{{1 2 2 3}}&{\it m}_{{1 2 3 3}}&0&0&0&0&\cdots\\
\noalign{\medskip}{\it m}_{{1 3}}&0&0&{\it m}_{{1 1 3}}&{\it m}_{{1 2 3}}&{\it m}_{{1 3 3}}&0&0&0&{\it m}_{{1 1 1 3}}&2~{\it m}_{{1 1 2 3}}&2~{\it m}_{{1 1 3 3}}&{\it m}_{{1 2 2 3}}&2~{\it m}_{{1 2 3 3}}&{\it m}_{{1 3 3 3}}&0&0&0&0&\cdots\\
\noalign{\medskip}{\it m}_{{2 2}}&0&0&{\it m}_{{1 2 2}}&{\it m}_{{2 2 2}}&{\it m}_{{2 2 3}}&0&0&0&{\it m}_{{1 1 2 2}}&2~{\it m}_{{1 2 2 2}}&2~{\it m}_{{1 2 2 3}}&{\it m}_{{2 2 2 2}}&2~{\it m}_{{2 2 2 3}}&{\it m}_{{2 2 3 3}}&0&0&0&0&\cdots\\
\noalign{\medskip}{\it m}_{{2 3}}&0&0&{\it m}_{{1 2 3}}&{\it m}_{{2 2 3}}&{\it m}_{{2 3 3}}&0&0&0&{\it m}_{{1 1 2 3}}&2~{\it m}_{{1 2 2 3}}&2~{\it m}_{{1 2 3 3}}&{\it m}_{{2 2 2 3}}&2~{\it m}_{{2 2 3 3}}&{\it m}_{{2 3 3 3}}&0&0&0&0&\cdots\\
\noalign{\medskip}{\it m}_{{3 3}}&0&0&{\it m}_{{1 3 3}}&{\it m}_{{2 3 3}}&{\it m}_{{3 3 3}}&0&0&0&{\it m}_{{1 1 3 3}}&2~{\it m}_{{1 2 3 3}}&2~{\it m}_{{1 3 3 3}}&{\it m}_{{2 2 3 3}}&2~{\it m}_{{2 3 3 3}}&{\it m}_{{3 3 3 3}}&0&0&0&0&\cdots\\
\noalign{\medskip}{\it m}_{{1 1 1}}&0&0&{\it m}_{{1 1 1 1}}&{\it m}_{{1 1 1 2}}&{\it m}_{{1 1 1 3}}&0&0&0&{\it m}_{{1 1 1 1 1}}&2~{\it m}_{{1 1 1 1 2}}&2~{\it m}_{{1 1 1 1 3}}&{\it m}_{{1 1 1 2 2}}&2~{\it m}_{{1 1 1 2 3}}&{\it m}_{{1 1 1 3 3}}&0&0&0&0&\cdots\\
\noalign{\medskip}{\it m}_{{1 1 2}}&0&0&{\it m}_{{1 1 1 2}}&{\it m}_{{1 1 2 2}}&{\it m}_{{1 1 2 3}}&0&0&0&{\it m}_{{1 1 1 1 2}}&2~{\it m}_{{1 1 1 2 2}}&2~{\it m}_{{1 1 1 2 3}}&{\it m}_{{1 1 2 2 2}}&2~{\it m}_{{1 1 2 2 3}}&{\it m}_{{1 1 2 3 3}}&0&0&0&0&\cdots\\
\noalign{\medskip}{\it m}_{{1 1 3}}&0&0&{\it m}_{{1 1 1 3}}&{\it m}_{{1 1 2 3}}&{\it m}_{{1 1 3 3}}&0&0&0&{\it m}_{{1 1 1 1 3}}&2~{\it m}_{{1 1 1 2 3}}&2~{\it m}_{{1 1 1 3 3}}&{\it m}_{{1 1 2 2 3}}&2~{\it m}_{{1 1 2 3 3}}&{\it m}_{{1 1 3 3 3}}&0&0&0&0&\cdots\\
\noalign{\medskip}{\it m}_{{1 2 2}}&0&0&{\it m}_{{1 1 2 2}}&{\it m}_{{1 2 2 2}}&{\it m}_{{1 2 2 3}}&0&0&0&{\it m}_{{1 1 1 2 2}}&2~{\it m}_{{1 1 2 2 2}}&2~{\it m}_{{1 1 2 2 3}}&{\it m}_{{1 2 2 2 2}}&2~{\it m}_{{1 2 2 2 3}}&{\it m}_{{1 2 2 3 3}}&0&0&0&0&\cdots\\
\noalign{\medskip}{\it m}_{{1 2 3}}&0&0&{\it m}_{{1 1 2 3}}&{\it m}_{{1 2 2 3}}&{\it m}_{{1 2 3 3}}&0&0&0&{\it m}_{{1 1 1 2 3}}&2~{\it m}_{{1 1 2 2 3}}&2~{\it m}_{{1 1 2 3 3}}&{\it m}_{{1 2 2 2 3}}&2~{\it m}_{{1 2 2 3 3}}&{\it m}_{{1 2 3 3 3}}&0&0&0&0&\cdots\\
\noalign{\medskip}{\it m}_{{1 3 3}}&0&0&{\it m}_{{1 1 3 3}}&{\it m}_{{1 2 3 3}}&{\it m}_{{1 3 3 3}}&0&0&0&{\it m}_{{1 1 1 3 3}}&2~{\it m}_{{1 1 2 3 3}}&2~{\it m}_{{1 1 3 3 3}}&{\it m}_{{1 2 2 3 3}}&2~{\it m}_{{1 2 3 3 3}}&{\it m}_{{1 3 3 3 3}}&0&0&0&0&\cdots\\
\noalign{\medskip}{\it m}_{{2 2 2}}&0&0&{\it m}_{{1 2 2 2}}&{\it m}_{{2 2 2 2}}&{\it m}_{{2 2 2 3}}&0&0&0&{\it m}_{{1 1 2 2 2}}&2~{\it m}_{{1 2 2 2 2}}&2~{\it m}_{{1 2 2 2 3}}&{\it m}_{{2 2 2 2 2}}&2~{\it m}_{{2 2 2 2 3}}&{\it m}_{{2 2 2 3 3}}&0&0&0&0&\cdots\\
\noalign{\medskip}{\it m}_{{2 2 3}}&0&0&{\it m}_{{1 2 2 3}}&{\it m}_{{2 2 2 3}}&{\it m}_{{2 2 3 3}}&0&0&0&{\it m}_{{1 1 2 2 3}}&2~{\it m}_{{1 2 2 2 3}}&2~{\it m}_{{1 2 2 3 3}}&{\it m}_{{2 2 2 2 3}}&2~{\it m}_{{2 2 2 3 3}}&{\it m}_{{2 2 3 3 3}}&0&0&0&0&\cdots\\
\noalign{\medskip}{\it m}_{{2 3 3}}&0&0&{\it m}_{{1 2 3 3}}&{\it m}_{{2 2 3 3}}&{\it m}_{{2 3 3 3}}&0&0&0&{\it m}_{{1 1 2 3 3}}&2~{\it m}_{{1 2 2 3 3}}&2~{\it m}_{{1 2 3 3 3}}&{\it m}_{{2 2 2 3 3}}&2~{\it m}_{{2 2 3 3 3}}&{\it m}_{{2 3 3 3 3}}&0&0&0&0&\cdots\\
\noalign{\medskip}{\it m}_{{3 3 3}}&0&0&{\it m}_{{1 3 3 3}}&{\it m}_{{2 3 3 3}}&{\it m}_{{3 3 3 3}}&0&0&0&{\it m}_{{1 1 3 3 3}}&2~{\it m}_{{1 2 3 3 3}}&2~{\it m}_{{1 3 3 3 3}}&{\it m}_{{2 2 3 3 3}}&2~{\it m}_{{2 3 3 3 3}}&{\it m}_{{3 3 3 3 3}}&0&0&0&0&\cdots\\
\noalign{\medskip}\vdots&\vdots&\vdots&\vdots&\vdots&\vdots&\vdots&\vdots&\vdots&\vdots&\vdots&\vdots&\vdots&\vdots&\vdots&\vdots&\vdots&\vdots&\vdots&~\\
\end{array} \right]
$$
\vspace*{5mm}
\end{table}