The Coeff(A,x,n) command computes the n-th coefficient of a matrix of polynomials A.

The Coeff[row](A,x,vn) command computes the vn[i]-th coefficient of A for row i. That is, the number of elements in the list vn must equal the number of rows in A.

The Coeff[column](A,x,vn) command computes the vn[i]-th coefficient of A for column i. That is, the number of elements in the list vn must equal the number of columns in A.

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

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

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

$\mathrm{seq}\left(\mathrm{Coeff}\left(A\,x\,i\right)\,i=0..2\right)$

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

$\mathrm{seq}\left(\mathrm{Coeff}\left[\mathrm{row}\right]\left(A\,x\,\left[i+1\,i\,i\right]\right)\,i=0..1\right)$

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

$\mathrm{seq}\left(\mathrm{Coeff}\left[\mathrm{column}\right]\left(A\,x\,\left[i+1\,i\,i\right]\right)\,i=0..1\right)$

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