Kalkulator Determinan Matriks
Hitung determinan matriks langkah demi langkah
Kalkulator akan menghitung determinan matriks (2x2, 3x3, 4x4, dll.) menggunakan ekspansi kofaktor, dengan menampilkan langkah-langkahnya.
Kalkulator terkait: Kalkulator Matriks Kofaktor
Masukan Anda
Hitung $$$\left|\begin{array}{ccc}1 & 2 & 2\\0 & 5 & 7\\1 & 1 & 1\end{array}\right|$$$.
Solusi
Kurangi baris $$$1$$$ dari baris $$$3$$$: $$$R_{3} = R_{3} - R_{1}$$$.
$$$\left|\begin{array}{ccc}1 & 2 & 2\\0 & 5 & 7\\1 & 1 & 1\end{array}\right| = \left|\begin{array}{ccc}1 & 2 & 2\\0 & 5 & 7\\0 & -1 & -1\end{array}\right|$$$
Kembangkan menurut kolom $$$1$$$:
$$$\left|\begin{array}{ccc}1 & 2 & 2\\0 & 5 & 7\\0 & -1 & -1\end{array}\right| = \left(1\right) \left(-1\right)^{1 + 1} \left|\begin{array}{cc}5 & 7\\-1 & -1\end{array}\right| + \left(0\right) \left(-1\right)^{2 + 1} \left|\begin{array}{cc}2 & 2\\-1 & -1\end{array}\right| + \left(0\right) \left(-1\right)^{3 + 1} \left|\begin{array}{cc}2 & 2\\5 & 7\end{array}\right| = \left|\begin{array}{cc}5 & 7\\-1 & -1\end{array}\right|$$$
Determinan matriks 2x2 adalah $$$\left|\begin{array}{cc}a & b\\c & d\end{array}\right| = a d - b c$$$.
$$$\left|\begin{array}{cc}5 & 7\\-1 & -1\end{array}\right| = \left(5\right)\cdot \left(-1\right) - \left(7\right)\cdot \left(-1\right) = 2$$$
Jawaban
$$$\left|\begin{array}{ccc}1 & 2 & 2\\0 & 5 & 7\\1 & 1 & 1\end{array}\right| = 2$$$A