G2.21a znaleźć macierz odwrotną

[kawafis44]

\(\displaystyle{ A=\left[\begin{array}{ccc}1&2&1\\-1&-1&0\\1&3&1\end{array}\right]}\)
\(\displaystyle{ A^{-1}=?}\)
\(\displaystyle{ adj(A)=\left[\begin{array}{ccc}\left|\begin{array}{ccc}-1&0\\3&1\end{array}\right|&-\left|\begin{array}{ccc}-1&0\\1&1\end{array}\right|&\left|\begin{array}{ccc}-1&-1\\1&3\end{array}\right|\\-\left|\begin{array}{ccc}2&1\\3&1\end{array}\right|&\left|\begin{array}{ccc}1&1\\1&1\end{array}\right|&-\left|\begin{array}{ccc}1&2\\1&3\end{array}\right|\\\left|\begin{array}{ccc}2&1\\-1&0\end{array}\right|&-\left|\begin{array}{ccc}1&1\\-1&0\end{array}\right|&\left|\begin{array}{ccc}1&2\\-1&-1\end{array}\right|\end{array}\right] = ft[\begin{array}{ccc}-1&1&-2\\1&0&-1\\1&1&1\end{array}\right]}\)
\(\displaystyle{ det(A)=\left|\begin{array}{ccc}1&2&1\\-1&-1&0\\1&3&1\end{array}\right| = 1-3+1+2=1 A^{-1}=\frac{1}{det(A)}\cdot adj(A) = \frac{1}{1}\cdot adj(A) = adj(A)}\)

podczas gdy w odpowiedziach jest \(\displaystyle{ A^{-1}=\left[\begin{array}{ccc}1&-1&-1\\-1&0&1\\2&1&-1\end{array}\right]}\)
co zrobiłem źle?

pozdrawiam!

[alia]

\(\displaystyle{ det(A) = -1-3+1+2 =-1}\)
ponadto
\(\displaystyle{ A^{-1} = \frac{1}{det(A)}\cdot adj(A)^T}\)