{x2 = 3*x4-2, x1 = -5*x4+3, x3 = -4*x4+2, x4 = x4}

I tried using matrix but it doesnt work either. This is what i did.

A:=matrix([[2,1,-1,3],[1,1,0,-1],[3,2,-2,1]]);
> b:=vector([2,-1,1]);
                           [2    1    -1     3]
                           [                  ]
                      A := [1    1     0    -1]
                           [                  ]
                           [3    2    -2     1]


                           b := [2, -1, 1]

> linsolve(A,b,'r');

              [3 - 5 _t[1], -4 + 6 _t[1], -_t[1], _t[1]]

> r;

                                  3

> linsolve(A,b,'r',v);

                [3 - 5 v[1], -4 + 6 v[1], -v[1], v[1]]