基本的な行列の問題

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

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

${\displaystyle =-2\left\{2\left(1+20\right)+2\left(4+15\right)-5\left(16-3\right)\right\}}$

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

${\displaystyle =-5\left\{-8\left(1+20\right)+2\left(3-5\right)-5\left(12+1\right)\right\}}$

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

${\displaystyle =-3\left\{-8\left(4+15\right)-2\left(3-5\right)-5\left(9+4\right)\right\}}$

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

${\displaystyle =7\left\{-8\left(16-3\right)-2\left(12+1\right)-2\left(9+4\right)\right\}}$

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