第16章 16.3

(1)

∣6324−6−12−235638401∣=∣−26−132010720−21−7608401∣=∣−26−1321072−21−76∣=∣−26−1323620057320∣=2∣36205732∣\begin{vmatrix} 6 & 3 & 2 & 4 \\ -6 & -1 & 2 & -2 \\ 3 & 5 & 6 & 3 \\ 8 & 4 & 0 & 1 \end{vmatrix} = \begin{vmatrix} -26 & -13 & 2 & 0 \\ 10 & 7 & 2 & 0 \\ -21 & -7 & 6 & 0 \\ 8 & 4 & 0 & 1 \end{vmatrix} = \begin{vmatrix} -26 & -13 & 2 \\ 10 & 7 & 2 \\ -21 & -7 & 6 \end{vmatrix} = \begin{vmatrix} -26 & -13 & 2 \\ 36 & 20 & 0 \\ 57 & 32 & 0 \end{vmatrix} =2\begin{vmatrix} 36 & 20 \\ 57 & 32 \end{vmatrix}

=2(36⋅32−20⋅57)=24=2(36\cdot32-20\cdot57)=24

(2)

∣3251−3−112211243−21∣=∣3251−9−5−90−4−3−9011−70∣=−∣−9−5−9−4−3−911−7∣=−∣−40−44−10−3011−7∣=∣−4−44−1−30∣\begin{vmatrix} 3 & 2 & 5 & 1 \\ -3 & -1 & 1 & 2 \\ 2 & 1 & 1 & 2 \\ 4 & 3 & -2 & 1 \end{vmatrix} = \begin{vmatrix} 3 & 2 & 5 & 1 \\ -9 & -5 & -9 & 0 \\ -4 & -3 & -9 & 0 \\ 1 & 1 & -7 & 0 \end{vmatrix} =-\begin{vmatrix} -9 & -5 & -9 \\ -4 & -3 & -9 \\ 1 & 1 & -7 \end{vmatrix} =-\begin{vmatrix} -4 & 0 & -44 \\ -1 & 0 & -30 \\ 1 & 1 & -7 \end{vmatrix} =\begin{vmatrix} -4 & -44 \\ -1 & -30 \end{vmatrix}

=−4⋅(−30)−(−1)⋅(−44)=76=-4\cdot(-30)-(-1)\cdot(-44)=76

(3)

∣1103−134223543−2−22∣=∣11030445015−20−5−2−7∣=∣44515−2−5−2−7∣=∣0−161315−2023−17∣=−∣−161323−17∣\begin{vmatrix} 1 & 1 & 0 & 3 \\ -1 & 3 & 4 & 2 \\ 2 & 3 & 5 & 4 \\ 3 & -2 & -2 & 2 \end{vmatrix} = \begin{vmatrix} 1 & 1 & 0 & 3 \\ 0 & 4 & 4 & 5 \\ 0 & 1 & 5 & -2 \\ 0 & -5 & -2 & -7 \end{vmatrix} = \begin{vmatrix} 4 & 4 & 5 \\ 1 & 5 & -2 \\ -5 & -2 & -7 \end{vmatrix} = \begin{vmatrix} 0 & -16 & 13 \\ 1 & 5 & -2 \\ 0 & 23 & -17 \end{vmatrix} =-\begin{vmatrix} -16 & 13 \\ 23 & -17 \end{vmatrix}

=−(−16⋅(−17)−13⋅23)=27=-(-16\cdot(-17)-13\cdot23)=27

(4)

∣0221202122011110∣=∣02210−20100−211110∣=−∣221−2010−21∣=−(4+4+4)=−12\begin{vmatrix} 0 & 2 & 2 & 1 \\ 2 & 0 & 2 & 1 \\ 2 & 2 & 0 & 1 \\ 1 & 1 & 1 & 0 \end{vmatrix} = \begin{vmatrix} 0 & 2 & 2 & 1 \\ 0 & -2 & 0 & 1 \\ 0 & 0 & -2 & 1 \\ 1 & 1 & 1 & 0 \end{vmatrix} =-\begin{vmatrix} 2 & 2 & 1 \\ -2 & 0 & 1 \\ 0 & -2 & 1 \end{vmatrix} =-(4+4+4)=-12

解説: r31bn1z