The GenerateEquations(A, v) command, generates a list of linear equations from the coefficient Matrix A, using the variable names given in v.

If the optional $mx1$ right-hand side Vector B is included in the calling sequence, then the list of linear equations is equivalent to the Matrix equation $A·x=B$, where the $x_i$ are equal to the corresponding $v_i$.  In this case, v must specify exactly n unknowns.

If the optional right-hand side Vector B is omitted in the calling sequence, and v specifies exactly n unknowns, then the right-hand sides of the m linear equations are set to zero.  The list of equations is then equivalent to $A·x=\mathrm{ZeroVector}\left(m\right)$.

If the optional right-hand side Vector B is omitted in the calling sequence, and v specifies exactly $n-1$ unknowns, then the right-hand sides of the m linear equations are taken from the last column of the Matrix A.  That is, the Matrix A is treated as an augmented matrix. The list of equations is then equivalent to $A_{1..\mathrm{-1},1..\mathrm{-2}}·x=A_{1..\mathrm{-1},\mathrm{-1}}$.

$\mathrm{with}\left(\mathrm{Student}\left[\mathrm{LinearAlgebra}\right]\right)\:$

$V≔⟨⟨1\,2\,3⟩\left|⟨4\,5\,6⟩\right|⟨7\,8\,0⟩⟩$

$V≔\left[\begin{array}{ccc}1& 4& 7\\ 2& 5& 8\\ 3& 6& 0\end{array}\right]$

$\mathrm{GenerateEquations}\left(V\,\left[x\,y\,z\right]\,⟨0\,-1\,3⟩\right)$

$\left[x+4y+7z=0\,2x+5y+8z=\mathrm{-1}\,3x+6y=3\right]$

$W≔⟨⟨1\,2⟩|⟨3\,4⟩⟩$

$W≔\left[\begin{array}{cc}1& 3\\ 2& 4\end{array}\right]$

$\mathrm{GenerateEquations}\left(⟨W|⟨-3\,2⟩⟩\,\left[a\,b\right]\right)$

$\left[a+3b=\mathrm{-3}\,2a+4b=2\right]$