Hey sirrelwood.

If your solution is correct, then yes your solution, is correct.

Checking with octave, I get the following:

>> A = [1, 2, -1; -1, -2, 3; 1, 1, 1]

A =

1 2 -1

-1 -2 3

1 1 1

>> b = [1; 0; -2]

b =

1

0

-2

>> A\b

ans =

-6.50000

4.00000

0.50000

The above confirms that the solution is unique however the actual solution obtained is very different.

The inverse of the matrix given by Octave is:

>> inv(A)

ans =

-2.50000 -1.50000 2.00000

2.00000 1.00000 -1.00000

0.50000 0.50000 0.00000