# Elementary Operation 1: Interchanging two rows

Consider again the linear system of equations associated to
Example1.
ORIGINAL AFTER INTERCHANGING E1 AND E4
100 x + 10 y + z - N = 0 - x - y + z = 1
15 x + 15 y + 15 z - N = 0 15 x + 15 y + 15 z - N = 0
x + 10 y + 100 z - N = 396 x + 10 y + 100 z - N = 396
- x - y + z = 1 100 x + 10 y + z - N = 0

The corresponding augmented matrices for the original (A) and the
transformed system (B) are:
[ 100 10 1 -1 0 ] [ -1 -1 1 0 1 ]
[ ] [ ]
[ 15 15 15 -1 0 ] [ 15 15 15 -1 0 ]
A := [ ] B := [ ]
[ 1 10 100 -1 396 ] [ 1 10 100 -1 396 ]
[ ] [ ]
[ -1 -1 1 0 1 ] [ 100 10 1 -1 0 ]

Clearly "A" and "B" have rows 1 and 4 interchanged but they both contain
the same information about the unknowns.