I have a C in $F_2^6$
$(x_1,x_2,x_3,x_4) \to (x_1,x_2,x_3,x_4,x_1+x_2,x_3+x_4)$
for $x = (1,0,1,1)$ i get $c = (1,0,1,1,1,0)$
we know that $$c = G . x$$
G is the Generator Matrix
in the solution G is $$ G = \left[\frac{I_4}{A}\right] = \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \\ \hline 1 & 1 & 0 & 0 \\ 0 & 0 & 1 & 1 \\ \end{bmatrix} $$
My problem is I want to get myself to the Matrix A in another word G! because i have only the solution without steps!