 Error, (in LinearAlgebra:-LinearSolve) inconsistent system - Maple Programming Help

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Error, (in LinearAlgebra:-LinearSolve) inconsistent system

 Description This error occurs when Maple does not find a mathematical solution to a matrix equation representing a system of linear equations.   Sometimes, there is no solution to a given problem, which is a legitimate result.  In this case, there is nothing to fix; this is Maple's response that there is no solution available.

Examples

In this example, $\mathrm{Mat}$ has all zero entries while  does not. The system  has no solution.

 > $\mathrm{with}\left(\mathrm{LinearAlgebra}\right):$
 > $\mathrm{eqs}≔\left[\mathrm{seq}\right]\left(\mathrm{eqn}\parallel i,i=1..16\right):$
 > $\left(\mathrm{Mat},\mathrm{Vec}\right)≔\mathrm{GenerateMatrix}\left(\mathrm{eqs},\left[a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p\right]\right);$
 ${\mathrm{Mat}}{,}{\mathrm{Vec}}{:=}\left[\begin{array}{c}{\mathrm{16 x 16}}{\mathrm{Matrix}}\\ {\mathrm{Data Type:}}{\mathrm{anything}}\\ {\mathrm{Storage:}}{\mathrm{rectangular}}\\ {\mathrm{Order:}}{\mathrm{Fortran_order}}\end{array}\right]{,}\left[\begin{array}{c}{\mathrm{1 .. 16}}{{\mathrm{Vector}}}_{{\mathrm{column}}}\\ {\mathrm{Data Type:}}{\mathrm{anything}}\\ {\mathrm{Storage:}}{\mathrm{rectangular}}\\ {\mathrm{Order:}}{\mathrm{Fortran_order}}\end{array}\right]$ (2.1)
 > $\mathrm{LinearSolve}\left(\mathrm{Mat},\mathrm{Vec}\right);$