Materi : Determinan tingkat N
Transformasikan Determinan Berikut ke dalam Determinan yang sama yang mempunyai tiga nol di kolom ketiga :
[tex] | - 2 \: \: 4 \ \: 1 \ \: 3| \\ |1 \: - 2 \: \: 2 \: \: 4| \\ |3 \: \: 1 \:- 3 \: \: 2| \\ |4 \: \: 3 \: - 2 \: - 1| [/tex]
Jawaban:
[tex]\large\text{$\begin{aligned}\left|\begin{matrix}-2 & 4 & 1 & 3 \\5 & -10 & \bf0 & -2 \\-3 & 13 & \bf0 & 11 \\0 & 11 & \bf0 & 5\end{matrix}\right|\end{aligned}$}[/tex]
Pembahasan
Transformasi Determinan Tingkat N
[tex]\large\text{$\begin{aligned}&\textsf{1. Baris ke-2: }B_2-2B_1\\&\left|\begin{matrix}-2 & 4 & 1 & 3 \\1 & -2 & 2 & 4 \\3 & 1 & -3 & 2 \\4 & 3 & -2 & -1\end{matrix}\right|\xrightarrow{B_2=B_2-2B_1}\left|\begin{matrix}-2 & 4 & 1 & 3 \\5 & -10 & 0 & -2 \\3 & 1 & -3 & 2 \\4 & 3 & -2 & -1\end{matrix}\right|\end{aligned}$}[/tex]
[tex]\large\text{$\begin{aligned}&\textsf{2. Baris ke-3: }B_3+3B_1\\&\left|\begin{matrix}-2 & 4 & 1 & 3 \\5 & -10 & 0 & -2 \\3 & 1 & -3 & 2 \\4 & 3 & -2 & -1\end{matrix}\right|\xrightarrow{B_3=B_3+3B_1}\left|\begin{matrix}-2 & 4 & 1 & 3 \\5 & -10 & 0 & -2 \\-3 & 13 & 0 & 11 \\4 & 3 & -2 & -1\end{matrix}\right|\end{aligned}$}[/tex]
[tex]\large\text{$\begin{aligned}&\textsf{3. Baris ke-4: }B_4+2B_1\\&\left|\begin{matrix}-2 & 4 & 1 & 3 \\5 & -10 & 0 & -2 \\-3 & 13 & 0 & 11 \\4 & 3 & -2 & -1\end{matrix}\right|\xrightarrow{B_4=B_4+2B_1}\left|\begin{matrix}-2 & 4 & 1 & 3 \\5 & -10 & \bf0 & -2 \\-3 & 13 & \bf0 & 11 \\0 & 11 & \bf0 & 5\end{matrix}\right|\end{aligned}$}[/tex]
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