Răspuns:
[tex]d\overset{L_1+L_2+L_3}{=}\begin{vmatrix}0 & 0 & 3x_3 & 0\\-2x_1 & x_2 & x_3 & x_4\\x_1 & -2x_2 & x_3 & x_4\\x_1 & x_2 & -2x_3 & x_4\end{vmatrix}=3x_3\begin{vmatrix}-2x_1 & x_2 & x_4\\x_1 & -2x_2 & x_4\\x_1 & x_2 & x_4\end{vmatrix}=\\\overset{L_1+L_2+L_3}{=}3x_3\begin{vmatrix}0 & 0 & 3x_4\\x_1 & -2x_2 & x_4\\x_1 & x_2 & x_4\end{vmatrix}=9x_3x_4\begin{vmatrix}x_1 & -2x_2\\x_1 & x_2\end{vmatrix}=27x_1x_2x_3x_4=-27[/tex]
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Răspuns:
[tex]d\overset{L_1+L_2+L_3}{=}\begin{vmatrix}0 & 0 & 3x_3 & 0\\-2x_1 & x_2 & x_3 & x_4\\x_1 & -2x_2 & x_3 & x_4\\x_1 & x_2 & -2x_3 & x_4\end{vmatrix}=3x_3\begin{vmatrix}-2x_1 & x_2 & x_4\\x_1 & -2x_2 & x_4\\x_1 & x_2 & x_4\end{vmatrix}=\\\overset{L_1+L_2+L_3}{=}3x_3\begin{vmatrix}0 & 0 & 3x_4\\x_1 & -2x_2 & x_4\\x_1 & x_2 & x_4\end{vmatrix}=9x_3x_4\begin{vmatrix}x_1 & -2x_2\\x_1 & x_2\end{vmatrix}=27x_1x_2x_3x_4=-27[/tex]
Explicație pas cu pas: