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YOU CAN DIVIDE EQN.I WITH 2 AND ADD TO EQN.III TO ELIMINATE X
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x - y + z = 2
-x + y + z = 4
-x + z = 2
augmented matrix is
1.....................-1.......................1.............................2
-1.....................1.......................1.............................4
-1.....................0.......................1.............................2
nr2=r2+r1 and nr3=r3+r1
1..................-1.................1.............2
1-1=0............1-1=0............1+1=2..........2+4=6
1-1=0...........-1+0=-1...........1+1=2..........2+2=4
nr2=r2/2....nr3=r3-r2
1....................-1...............1..............2
0/2=0.............0/2=0..............2/2=1........6/2=3
0-0=0............-1-0=-1..............2-2=0.......4-6=-2
nr1=r1-r3-r2.......nr2=2r2........nr3=-r3
1-0-0=1............-1+1-0=0.........1-0-1=0.......2+2-3=1
0.....................0...................1............3
0.....................1...................0.............2
exchange r2 and r3
1....0........0.......1
0....1........0.......2
0....0........1.......3
hence x=1......y=2.....z=3
