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[NICO97]

Hello,
I'm using the rref fonction and i'm surprised by the result. I need to understand what le rref fonction do.

I'd like to solve AX=B with A=
1 1 0 0
0 1 1 0
0 0 1 1
1 0 0 1 and B = a,b,a,b

So i'm define the matrix below:
1 1 0 0 a
0 1 1 0 b
0 0 1 1 a
1 0 0 1 b
and after many elementary manipulations on the lines, in found:
1 0 0 1 2a-b
0 1 0 -1 b-a
0 0 1 1 a
0 0 0 0 2b-2a
I can see, then, that the equation don't have any solution, except if a=b.

But when i use the rref command on the same matrix, i get:
1 0 0 1 a
0 1 0 -1 a-b
0 0 1 1 -a+2b
0 0 0 0 1
Wich is diff?rent, and would show that there are no solution, in any case.

If someone could help me to understand what the machine do, i'd be glad.

Thanks by advance,