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[tex]\displaystyle \begin{vmatrix}x-1 & 4 & -1\\ 1 & x+2 & 1\\ 2x-4 & 4 & x-4\end{vmatrix}=0[/tex]
[tex]\displaystyle \begin{vmatrix}x-1 & 4 & -1\\ 1 & x+2 & 1\\ 2x-4 & 4 & x-4\end{vmatrix}=0[/tex]
Verified answer
Jawab:
x = {-2, 0, 3}
Penjelasan dengan langkah-langkah:
Determinan matriks 3×3
Dikarenakan . . .
[tex]\displaystyle\begin{vmatrix}m & n & p\\ q & r & s\\ x & y & z\end{vmatrix}\\\\=m\begin{vmatrix}r & s\\ y & z\end{vmatrix}-n\begin{vmatrix}q & s\\ x & z\end{vmatrix}+p\begin{vmatrix}q & r\\ x &y\end{vmatrix}\\\\=m(rz-sy)-n(qz-sx)+p(qy-rx)[/tex]
maka
[tex]\displaystyle\begin{vmatrix}x-1 & 4 & -1\\ 1 & x+2 & 1\\ 2x-4 & 4 & x-4\end{vmatrix}=0\\\\x-1\begin{vmatrix}x+2 & 1\\4 & x-4\end{vmatrix}-4\begin{vmatrix}1 & 1\\ 2x-4 & x-4\end{vmatrix}-1\begin{vmatrix}1 & x+2\\ 2x-4 & 4\end{vmatrix}=0\\\\((x-1)((x+2)(x-4)-4))-(4(x-4-(2x-4)))-(4-(x+2)(2x-4))=0\\((x-1)(x^2-2x-8-4))-(4(x-4-2x+4))-(4-(2x^2-8))=0\\((x-1)(x^2-2x-12))-(4(-x))-(4-2x^2+8)=0\\x^3-2x^2-12x-x^2+2x+12+4x-4+2x^2-8=0\\x^3-x^2-6x=0\\x(x^2-x-6)=0\\x(x-3)(x+2)=0\\x=\bf\{-2,0,3\}[/tex]
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