`A=((1,2,-1),(3,5,-1),(-2,-1,-2)),` `X=((x),(y),(z)),` and `C=((6),(2),(4))` 

Using Scientific Notebook, we find the inverse of A to be:

`A^-1=((5.5,-2.5,-1.5),(-4,2,1),(-3.5,1.5,0.5))`

(We could have used Gauss-Jordan Elimination if we need to show all steps.)

So the solution to the system of equations is:

`X=A^-1C`

`=((5.5,-2.5,-1.5),(-4,2,1),(-3.5,1.5,0.5))((6),(2),(4))`

`=((22),(-16),(-16))`

Check:

`22 + 2(-16) - (-16) = 6` [Checks OK]

`3(22) + 5(-16) - (-16) = 2` [Checks OK]

`-2(22) - (16) - 2(-16) = 4` [Checks OK]

So the solution is `x = 22`, `y = -16` and `z = -16`.