> #Rueckwaertselimination, ueberschreibt b;
with(LinearAlgebra):
> ruecksubs:=proc(U::Matrix,b::Vector) 
local j,k,n,r; 
r:=0; 
n:=Dimension(b); 
for j from 1 by 1 to n do  
  if U[j,j] =0 then r:=1; end if 
end do; 
if r=1 then print(`Matrix nicht invertierbar`);
else 
for j from n by (-1) to 1 do 
   for k from n by (-1) to j+1 do b[j]:=b[j] - U[j,k]*b[k]; end do; 
   b[j]:=b[j]/U[j,j]; 
end do; 
print(b); 
end if;
end proc:

> A:=Matrix([[1.,2.,3.,4.],[0,5.,6.,7.],[0,0,0.,9.],[0,0,0,10.]]);   c:=Vector([1,2,3,4]);
> ruecksubs(A,c);

                   Matrix nicht invertierbar
>