基本的な行列の問題

${\displaystyle =5\times {\left(-1\right)}^{1+2}\left|\begin{array}{ccc}3& 6& 2\\ 4& 8& 7\\ 7& 2& 5\end{array}\right|}$${\displaystyle +8\times {\left(-1\right)}^{2+2}\left|\begin{array}{ccc}2& 11& 3\\ 4& 8& 7\\ 7& 2& 5\end{array}\right|}$${\displaystyle +12\times {\left(-1\right)}^{3+2}\left|\begin{array}{ccc}2& 11& 3\\ 3& 6& 2\\ 7& 2& 5\end{array}\right|}$${\displaystyle +9\times {\left(-1\right)}^{4+2}\left|\begin{array}{ccc}2& 11& 3\\ 3& 6& 2\\ 4& 8& 7\end{array}\right|}$ ･･･（1）

${\displaystyle =-5\left\{6{\left(-1\right)}^{1+2}\left|\begin{array}{cc}4& 7\\ 7& 5\end{array}\right|+8{\left(-1\right)}^{2+2}\left|\begin{array}{cc}3& 2\\ 7& 5\end{array}\right|+2{\left(-1\right)}^{3+2}\left|\begin{array}{cc}3& 2\\ 4& 7\end{array}\right|\right\}}$

${\displaystyle =-5\left\{-6\left(20-49\right)+8\left(15-14\right)-2\left(21-8\right)\right\}}$

${\displaystyle =8\left\{11{\left(-1\right)}^{1+2}\left|\begin{array}{cc}4& 7\\ 7& 5\end{array}\right|+8{\left(-1\right)}^{2+2}\left|\begin{array}{cc}2& 3\\ 7& 5\end{array}\right|+2{\left(-1\right)}^{3+2}\left|\begin{array}{cc}2& 3\\ 4& 7\end{array}\right|\right\}}$

${\displaystyle =8\left\{-11\left(20-49\right)+8\left(10-21\right)-2\left(14-12\right)\right\}}$

${\displaystyle =8\left\{-11\times \left(-29\right)+8\times \left(-11\right)-2\times 2\right\}}$

${\displaystyle =-12\left\{11{\left(-1\right)}^{1+2}\left|\begin{array}{cc}3& 2\\ 7& 5\end{array}\right|+6{\left(-1\right)}^{2+2}\left|\begin{array}{cc}2& 3\\ 7& 5\end{array}\right|+2{\left(-1\right)}^{3+2}\left|\begin{array}{cc}2& 3\\ 3& 2\end{array}\right|\right\}}$

${\displaystyle =-12\left\{-11\left(15-14\right)+8\left(10-21\right)-2\left(4-9\right)\right\}}$

${\displaystyle =9\left\{11{\left(-1\right)}^{1+2}\left|\begin{array}{cc}3& 2\\ 4& 7\end{array}\right|+6{\left(-1\right)}^{2+2}\left|\begin{array}{cc}2& 3\\ 4& 7\end{array}\right|+8{\left(-1\right)}^{3+2}\left|\begin{array}{cc}2& 3\\ 3& 2\end{array}\right|\right\}}$

${\displaystyle =9\left\{-11\left(21-8\right)+6\left(14-12\right)-8\left(4-9\right)\right\}}$

${\displaystyle 5{\left(-1\right)}^{1+2}\left|\begin{array}{ccc}3& 6& 2\\ 4& 8& 7\\ 7& 2& 5\end{array}\right|}$${\displaystyle +8\times {\left(-1\right)}^{2+2}\left|\begin{array}{ccc}2& 11& 3\\ 4& 8& 7\\ 7& 2& 5\end{array}\right|}$${\displaystyle +12\times {\left(-1\right)}^{3+2}\left|\begin{array}{ccc}2& 11& 3\\ 3& 6& 2\\ 7& 2& 5\end{array}\right|}$${\displaystyle +9\times {\left(-1\right)}^{4+2}\left|\begin{array}{ccc}2& 11& 3\\ 3& 6& 2\\ 4& 8& 7\end{array}\right|}$