Thread: Gaussian elimination

I have a little problem with this exercise:

Consider system of 4 equations in 4 variables over GF(2).





Using Gaussian elimination we get:





How can I show this?

Use bases:
.
Then write equations in matrix form:

|1 0 0 1 1 1 1 0 1 0 1|
|1 1 1 0 0 1 0 1 1 0 1|
|1 1 0 1 0 1 1 0 0 1 1| = A (sorry for that form - latex command doesn't work)
|0 1 1 1 1 0 0 0 0 0 1|

And now bring A into the row echelon form using Gaussian elimination.
You get then

But is not the same like Yours.

Thanks. I check this.

You should very carefully examine papers about Mutants.