> with(LinearAlgebra):
> sols:=solve({2*x-y+3*z=1, x+y+z=2, x+y-2*z=1},{x,y,z});
                         /    10      1      5\ 
                sols := { y = --, z = -, x = - }
                         \    9       3      9/ 
> x:=subs(sols,x);
                                  5
                             x := -
                                  9
> x:='x';
                             x := x
> eq[1]:=a*x+y+z=1;
                    eq[1] := a x + y + z = 1
> eq[2]:=2*x-(1-a)*y+z=1;
                eq[2] := 2 x - (1 - a) y + z = 1
> eq[3]:=x+y-z=0;
                     eq[3] := x + y - z = 0
> solve({eq[1],eq[2],eq[3]},{x,y,z});
               /      2          1          1  \ 
              { z = -----, x = -----, y = ----- }
               \    a + 3      a + 3      a + 3/ 
> eq[1]:=subs(a=-3,eq[1]);
                   eq[1] := -3 x + y + z = 1
> eq[2]:=subs(a=-3,eq[2]);
                   eq[2] := 2 x - 4 y + z = 1
> eq[3]:=subs(a=-3,eq[3]);
                     eq[3] := x + y - z = 0
> solve({eq[1],eq[2],eq[3]},{x,y,z});
> 
> ###########################################################
> A:=<<1,1,1>|<2,1,1>|<0,1,1>>;
A:=[Typesetting:-mtable(Typesetting:-mtr(Typesetting:-mtd(1), 

  Typesetting:-mtd(2), Typesetting:-mtd(0)), Typesetting:-mtr(

  Typesetting:-mtd(1), Typesetting:-mtd(1), Typesetting:-mtd(1)), 

  Typesetting:-mtr(Typesetting:-mtd(1), Typesetting:-mtd(1), 

  Typesetting:-mtd(1)))]
> b:=<0,0,0>;
b:=[Typesetting:-mtable(Typesetting:-mtr(Typesetting:-mtd(0)), 

  Typesetting:-mtr(Typesetting:-mtd(0)), Typesetting:-mtr(Typesetting:-mtd(0)))

  ]
> LinearSolve(A,b,free='t');
[Typesetting:-mtable(Typesetting:-mtr(Typesetting:-mtd(uminus02 t[3])), 

  Typesetting:-mtr(Typesetting:-mtd(t[3])), 

  Typesetting:-mtr(Typesetting:-mtd(t[3])))]
> NullSpace(A);
{[Typesetting:-mtable(Typesetting:-mtr(Typesetting:-mtd(&minus;2)), 

  Typesetting:-mtr(Typesetting:-mtd(1)), Typesetting:-mtr(Typesetting:-mtd(1)))

  ]}
> Determinant(A);
                               0
>