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.