The Lcoeff(A,x) command computes the leading coefficient of a matrix of polynomials A.

The Lcoeff[row](A,x) command computes the leading row coefficient of A.  That is, it computes a matrix with rows that are the leading coefficient of each row of A.

The Lcoeff[column](A,x) command computes the leading column coefficient of A.

The Tcoeff(A,x), Tcoeff[row](A,x), and Tcoeff[column](A,x) commands compute the trailing coefficient, trailing row coefficient, and trailing column coefficients of A, respectively.

$\mathrm{with}\left(\mathrm{MatrixPolynomialAlgebra}\right)\:$

$A≔⟨⟨3+x\,4\,x^2-1⟩\left|⟨1\,x\,4⟩\right|⟨-4x^3\,2x\,-x^3⟩⟩$

$A≔\left[\begin{array}{ccc}3+x& 1& -4x^3\\ 4& x& 2x\\ x^2-1& 4& -x^3\end{array}\right]$

$\mathrm{Lcoeff}\left(A\,x\right)$

$\left[\begin{array}{ccc}0& 0& \mathrm{-4}\\ 0& 0& 0\\ 0& 0& \mathrm{-1}\end{array}\right]$

$\mathrm{Lcoeff}\left[\mathrm{row}\right]\left(A\,x\right)$

$\left[\begin{array}{ccc}0& 0& \mathrm{-4}\\ 0& 1& 2\\ 0& 0& \mathrm{-1}\end{array}\right]$

$\mathrm{Lcoeff}\left[\mathrm{column}\right]\left(A\,x\right)$

$\left[\begin{array}{ccc}0& 0& \mathrm{-4}\\ 0& 1& 0\\ 1& 0& \mathrm{-1}\end{array}\right]$

$\mathrm{Tcoeff}\left(A\,x\right)$

$\left[\begin{array}{ccc}3& 1& 0\\ 4& 0& 0\\ \mathrm{-1}& 4& 0\end{array}\right]$

$\mathrm{Tcoeff}\left[\mathrm{row}\right]\left(A\,x\right)$

$\left[\begin{array}{ccc}3& 1& 0\\ 4& 0& 0\\ \mathrm{-1}& 4& 0\end{array}\right]$

$\mathrm{Tcoeff}\left[\mathrm{column}\right]\left(A\,x\right)$

$\left[\begin{array}{ccc}3& 1& 0\\ 4& 0& 2\\ \mathrm{-1}& 4& 0\end{array}\right]$