SOLUTION: solve the system of equations by augmented matrix: 2x-y+z=1 x-y+z=-1 x-2y+z=2

Question 360033: solve the system of equations by augmented matrix:
2x-y+z=1
x-y+z=-1
x-2y+z=2
Answer by Jk22(389) (Show Source): You can put this solution on YOUR website!
Remark : (inspired by a comment)

Note that the RHS is not linear but affine, hence different from eigenvalue-like problems (1x, -1y, 2z)*, hence the last column cannot be put on the in diagonal on the LHS :

2 -1 +1 1 | -2last
1 -1 +1 -1 | -last
1 -2 +1 2

0 3 -1 -3 | -3mid
0 1 0 -3
1 -2 1 2

0 0 -1 6
0 1 0 -3
1 -2 1 2 | +2mid + first

0 0 -1 6
0 1 0 -3
1 0 0 2

=> x = 2, y = -3, z = -6

Verification :

2x-y+z = 4 + 3 - 6 = 7 - 6 = 1
x-y+z = 2 + 3 -6 = 5 - 6 = -1
x-2y+z = 2 + 6 -6 = 2
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