> #3.2-14 solved with maple
> macro(swap=linalg[swaprow]);macro(mult=linalg[mulrow]);
> macro(combo=linalg[addrow]);
> A1:=Matrix([[3,-6,-2,1],[2,-4,1,17],[1,-2,-2,-9]]);

                           [3    -6    -2     1]
                           [                   ]
                     A1 := [2    -4     1    17]
                           [                   ]
                           [1    -2    -2    -9]

> # last frame in one step
> linalg[rref](A1);

                         [1    -2    0    5]
                         [                 ]
                         [0     0    1    7]
                         [                 ]
                         [0     0    0    0]

> # Frame sequence A1, A2, A3, A4, ...
> A2:=swap(A1,1,3);

                           [1    -2    -2    -9]
                           [                   ]
                     A2 := [2    -4     1    17]
                           [                   ]
                           [3    -6    -2     1]

> A3:=combo(A2,1,2,-2);

                           [1    -2    -2    -9]
                           [                   ]
                     A3 := [0     0     5    35]
                           [                   ]
                           [3    -6    -2     1]

> A4:=combo(A3,1,3,-3);

                           [1    -2    -2    -9]
                           [                   ]
                     A4 := [0     0     5    35]
                           [                   ]
                           [0     0     4    28]

> # Col 1 is the first col of the identity matrix
> # Proceed to make col 3 the second col of the 
> # identity matrix. Then the last frame is found
> # which should equal rref(A1)
> # make a leading 1 in row 2
> A5:=combo(A4,3,2,-1);

                           [1    -2    -2    -9]
                           [                   ]
                     A5 := [0     0     1     7]
                           [                   ]
                           [0     0     4    28]

> A6:=combo(A5,2,3,-4);

                           [1    -2    -2    -9]
                           [                   ]
                     A6 := [0     0     1     7]
                           [                   ]
                           [0     0     0     0]

> A7:=combo(A6,2,1,2);

                            [1    -2    0    5]
                            [                 ]
                      A7 := [0     0    1    7]
                            [                 ]
                            [0     0    0    0]

> # last frame test passes
> linalg[rref](A1);

                         [1    -2    0    5]
                         [                 ]
                         [0     0    1    7]
                         [                 ]
                         [0     0    0    0]

> # To finish the solution, translate to equations
> # and apply the Last Frame Algorithm.
> # This part of the solution is done by hand.
> 
# Answer check
A:=Matrix([[3,-6,-2],[2,-4,1],[1,-2,-2]]);
b:=<1,17,-9>;
linalg[linsolve](A,b);
LinearAlgebra[LinearSolve](A,b);