Solving linear systems Ax = b

The coefficient matrix and the data 
- change to suit yourself
- enclosing things in the ‘MatrixForm’ command is just to format output nicely.  Try removing this command to see what the output looks like

MatrixForm[A={{2,-2,4},{1,1,-2},{3,-3,6}}]
MatrixForm[b={1,0,-1}]

The augmented matrix (I’d love to have a better way to do this in Mathematica)

MatrixForm[Aaug = Transpose[Append[Transpose[A],b]]]

Put the matrix in reduced echelon form.

MatrixForm[RowReduce[Aaug]]