高専の数学解説

第16章 16.13

(1)

∣2−100−12−100−12−100−12∣=2∣2−10−12−10−12∣+(−1)∣−12−10−12∣\begin{vmatrix} 2 & -1 & 0 & 0 \\ -1 & 2 & -1 & 0 \\ 0 & -1 & 2 & -1 \\ 0 & 0 & -1 & 2 \end{vmatrix} = 2\begin{vmatrix} 2 & -1 & 0 \\ -1 & 2 & -1 \\ 0 & -1 & 2 \end{vmatrix} + (-1)\begin{vmatrix} -1 & 2 & -1 \\ 0 & -1 & 2 \end{vmatrix}

=2(8−2−2)+(−4+1)=8−3=5= 2(8 - 2 - 2) + (-4 + 1) = 8 - 3 = 5

(2)

∣9543418286−43−291347∣=∣9543418286−43−20804∣=4∣9543418286−43−20201∣\begin{vmatrix} 9 & 5 & 4 & 3 \\ 4 & 18 & 2 & 8 \\ 6 & -4 & 3 & -2 \\ 9 & 13 & 4 & 7 \end{vmatrix} = \begin{vmatrix} 9 & 5 & 4 & 3 \\ 4 & 18 & 2 & 8 \\ 6 & -4 & 3 & -2 \\ 0 & 8 & 0 & 4 \end{vmatrix} = 4\begin{vmatrix} 9 & 5 & 4 & 3 \\ 4 & 18 & 2 & 8 \\ 6 & -4 & 3 & -2 \\ 0 & 2 & 0 & 1 \end{vmatrix}

=4∣9−140422060300201∣= 4\begin{vmatrix} 9 & -1 & 4 & 0 \\ 4 & 2 & 2 & 0 \\ 6 & 0 & 3 & 0 \\ 0 & 2 & 0 & 1 \end{vmatrix}

=12∣9−14422201∣=12∣020201021∣=12∣1−102∣=24= 12\begin{vmatrix} 9 & -1 & 4 \\ 4 & 2 & 2 \\ 2 & 0 & 1 \end{vmatrix} = 12\begin{vmatrix} 0 & 2 & 0 \\ 2 & 0 & 1 \\ 0 & 2 & 1 \end{vmatrix} = 12\begin{vmatrix} 1 & -1 \\ 0 & 2 \end{vmatrix} = 24

解説: r31bn1z