Ob das hilfreich ist?
EDIT: Antwort auf Fragestellung im Duplikat im 1. Kommentar.
Gaussalgorithmus: 1/256*A
$$ \begin{pmatrix}4 & 1 & \frac{1}{4} & \frac{1}{16} & \frac{1}{64} & \frac{1}{256} & \frac{1}{64}\cr -4 & 1 & -\frac{1}{4} & \frac{1}{16} & -\frac{1}{64} & \frac{1}{256} & \frac{1}{64}\cr 5 & 1 & \frac{3}{16} & \frac{1}{32} & \frac{1}{256} & 0 & -\frac{1}{128}\cr 5 & -1 & \frac{3}{16} & -\frac{1}{32} & \frac{1}{256} & 0 & -\frac{1}{256}\cr 5 & \frac{3}{4} & \frac{3}{32} & \frac{1}{128} & 0 & 0 & \frac{1}{256}\cr -5 & \frac{3}{4} & -\frac{3}{32} & \frac{1}{128} & 0 & 0 & 0\end{pmatrix} $$
$$A[2]=4*A[2]+4*A[1]$$
$$A[3]=4*A[3]-5*A[1]$$
$$A[4]=4*A[4]-5*A[1]$$
$$A[5]=4*A[5]-5*A[1]$$
$$A[6]=4*A[6]+5*A[1]$$
$$\begin{pmatrix}4 & 1 & \frac{1}{4} & \frac{1}{16} & \frac{1}{64} & \frac{1}{256} & \frac{1}{64}\cr 0 & 8 & 0 & \frac{1}{2} & 0 & \frac{1}{32} & \frac{1}{8}\cr 0 & -1 & -\frac{1}{2} & -\frac{3}{16} & -\frac{1}{16} & -\frac{5}{256} & -\frac{7}{64}\cr 0 & -9 & -\frac{1}{2} & -\frac{7}{16} & -\frac{1}{16} & -\frac{5}{256} & -\frac{3}{32}\cr 0 & -2 & -\frac{7}{8} & -\frac{9}{32} & -\frac{5}{64} & -\frac{5}{256} & -\frac{1}{16}\cr 0 & 8 & \frac{7}{8} & \frac{11}{32} & \frac{5}{64} & \frac{5}{256} & \frac{5}{64}\end{pmatrix}$$
$$A[3]=8*A[3]+1*A[2]$$
$$A[4]=8*A[4]+9*A[2]$$
$$A[5]=8*A[5]+2*A[2]$$
$$A[6]=8*A[6]-8*A[2]$$
$$\begin{pmatrix}4 & 1 & \frac{1}{4} & \frac{1}{16} & \frac{1}{64} & \frac{1}{256} & \frac{1}{64}\cr 0 & 8 & 0 & \frac{1}{2} & 0 & \frac{1}{32} & \frac{1}{8}\cr 0 & 0 & -4 & -1 & -\frac{1}{2} & -\frac{1}{8} & -\frac{3}{4}\cr 0 & 0 & -4 & 1 & -\frac{1}{2} & \frac{1}{8} & \frac{3}{8}\cr 0 & 0 & -7 & -\frac{5}{4} & -\frac{5}{8} & -\frac{3}{32} & -\frac{1}{4}\cr 0 & 0 & 7 & -\frac{5}{4} & \frac{5}{8} & -\frac{3}{32} & -\frac{3}{8}\end{pmatrix}$$
$$A[4]=-4*A[4]+4*A[3]$$
$$A[5]=-4*A[5]+7*A[3]$$
$$A[6]=-4*A[6]-7*A[3]$$
$$\begin{pmatrix}4 & 1 & \frac{1}{4} & \frac{1}{16} & \frac{1}{64} & \frac{1}{256} & \frac{1}{64}\cr 0 & 8 & 0 & \frac{1}{2} & 0 & \frac{1}{32} & \frac{1}{8}\cr 0 & 0 & -4 & -1 & -\frac{1}{2} & -\frac{1}{8} & -\frac{3}{4}\cr 0 & 0 & 0 & -8 & 0 & -1 & -\frac{9}{2}\cr 0 & 0 & 0 & -2 & -1 & -\frac{1}{2} & -\frac{17}{4}\cr 0 & 0 & 0 & 12 & 1 & \frac{5}{4} & \frac{27}{4}\end{pmatrix}$$
$$A[5]=-8*A[5]+2*A[4]$$
$$A[6]=-8*A[6]-12*A[4]$$
$$\begin{pmatrix}4 & 1 & \frac{1}{4} & \frac{1}{16} & \frac{1}{64} & \frac{1}{256} & \frac{1}{64}\cr 0 & 8 & 0 & \frac{1}{2} & 0 & \frac{1}{32} & \frac{1}{8}\cr 0 & 0 & -4 & -1 & -\frac{1}{2} & -\frac{1}{8} & -\frac{3}{4}\cr 0 & 0 & 0 & -8 & 0 & -1 & -\frac{9}{2}\cr 0 & 0 & 0 & 0 & 8 & 2 & 25\cr 0 & 0 & 0 & 0 & -8 & 2 & 0\end{pmatrix}$$
$$A[6]=8*A[6]+8*A[5]$$
$$A[6]=A[6]/A[6,6]$$
$$\begin{pmatrix}4 & 1 & \frac{1}{4} & \frac{1}{16} & \frac{1}{64} & \frac{1}{256} & \frac{1}{64}\cr 0 & 8 & 0 & \frac{1}{2} & 0 & \frac{1}{32} & \frac{1}{8}\cr 0 & 0 & -4 & -1 & -\frac{1}{2} & -\frac{1}{8} & -\frac{3}{4}\cr 0 & 0 & 0 & -8 & 0 & -1 & -\frac{9}{2}\cr 0 & 0 & 0 & 0 & 8 & 2 & 25\cr 0 & 0 & 0 & 0 & 0 & 1 & \frac{25}{4}\end{pmatrix}$$
Rücksubstitution...
$$A[1]=1/256*A[6]-1*A[1]$$
$$A[2]=1/32*A[6]-1*A[2]$$
$$A[3]=-1/8*A[6]-1*A[3]$$
$$A[4]=-1*A[6]-1*A[4]$$
$$A[5]=2*A[6]-1*A[5]$$
$$A[5]=A[5]/A[5,5]$$
$$\begin{pmatrix}-4 & -1 & -\frac{1}{4} & -\frac{1}{16} & -\frac{1}{64} & 0 & \frac{9}{1024}\cr 0 & -8 & 0 & -\frac{1}{2} & 0 & 0 & \frac{9}{128}\cr 0 & 0 & 4 & 1 & \frac{1}{2} & 0 & -\frac{1}{32}\cr 0 & 0 & 0 & 8 & 0 & 0 & -\frac{7}{4}\cr 0 & 0 & 0 & 0 & 1 & 0 & \frac{25}{16}\cr 0 & 0 & 0 & 0 & 0 & 1 & \frac{25}{4}\end{pmatrix}$$
$$A[1]=-1/64*A[5]-1*A[1]$$
$$A[3]=1/2*A[5]-1*A[3]$$
$$A[4]=A[4]/A[4,4]$$
$$\begin{pmatrix}4 & 1 & \frac{1}{4} & \frac{1}{16} & 0 & 0 & -\frac{17}{512}\cr 0 & -8 & 0 & -\frac{1}{2} & 0 & 0 & \frac{9}{128}\cr 0 & 0 & -4 & -1 & 0 & 0 & \frac{13}{16}\cr 0 & 0 & 0 & 1 & 0 & 0 & -\frac{7}{32}\cr 0 & 0 & 0 & 0 & 1 & 0 & \frac{25}{16}\cr 0 & 0 & 0 & 0 & 0 & 1 & \frac{25}{4}\end{pmatrix}$$
$$A[1]=1/16*A[4]-1*A[1]$$
$$A[2]=-1/2*A[4]-1*A[2]$$
$$A[3]=-1*A[4]-1*A[3]$$
$$A[3]=A[3]/A[3,3]$$
$$\begin{pmatrix}-4 & -1 & -\frac{1}{4} & 0 & 0 & 0 & \frac{5}{256}\cr 0 & 8 & 0 & 0 & 0 & 0 & \frac{5}{128}\cr 0 & 0 & 1 & 0 & 0 & 0 & -\frac{19}{128}\cr 0 & 0 & 0 & 1 & 0 & 0 & -\frac{7}{32}\cr 0 & 0 & 0 & 0 & 1 & 0 & \frac{25}{16}\cr 0 & 0 & 0 & 0 & 0 & 1 & \frac{25}{4}\end{pmatrix}$$
$$A[1]=-1/4*A[3]-1*A[1]$$
$$A[2]=A[2]/A[2,2]$$
$$\begin{pmatrix}4 & 1 & 0 & 0 & 0 & 0 & \frac{9}{512}\cr 0 & 1 & 0 & 0 & 0 & 0 & \frac{5}{1024}\cr 0 & 0 & 1 & 0 & 0 & 0 & -\frac{19}{128}\cr 0 & 0 & 0 & 1 & 0 & 0 & -\frac{7}{32}\cr 0 & 0 & 0 & 0 & 1 & 0 & \frac{25}{16}\cr 0 & 0 & 0 & 0 & 0 & 1 & \frac{25}{4}\end{pmatrix}$$
$$A[1]=1*A[2]-1*A[1]$$
$$A[1]=A[1]/A[1,1]$$
$$\begin{pmatrix}1 & 0 & 0 & 0 & 0 & 0 & \frac{13}{4096}\cr 0 & 1 & 0 & 0 & 0 & 0 & \frac{5}{1024}\cr 0 & 0 & 1 & 0 & 0 & 0 & -\frac{19}{128}\cr 0 & 0 & 0 & 1 & 0 & 0 & -\frac{7}{32}\cr 0 & 0 & 0 & 0 & 1 & 0 & \frac{25}{16}\cr 0 & 0 & 0 & 0 & 0 & 1 & \frac{25}{4}\end{pmatrix} $$