DETERMINANT OF A MATRIX / DETERMINAN MATRIKS

Determinant Matrix 2×2 Calculator

Kalkulator Determinan Matriks 2×2

Determinant

Determinant Matrix 3×3 Calculator

Kalkulator Determinan Matriks 3×3

Determinant

Determinant of Matrix 2×2 is
Determinan Mtariks 2×2 adalah
$\begin{vmatrix} a & b \\ c & d \end{vmatrix} =ad-bc$

Determinant of Matrix 3×3 is
Determinan Mtariks 3×3 adalah
$\begin{vmatrix} a & b & c \\ d & e & f \\ g & h & i \end{vmatrix} \\ =aei+bfg+cdh-gec-hfa-idb$

For Example / Contoh:
Find the determinant of the matrix below:
Carilah nilai determinan dari matriks berikut:
$\begin{pmatrix} 2 & -1 \\ 1 & 3 \end{pmatrix}$

$\begin{pmatrix} 1 & 3 & 2 \\ 2 & -1 & 2 \\ 2 & 2 & 1 \end{pmatrix}$

Solution / Jawaban:
$\begin{vmatrix} 2 & -1 \\ 1 & 3 \end{vmatrix}=2.3-1.(-1)=6+1=7$

$\begin{vmatrix} 1 & 3 & 2 \\ 2 & -1 & 2 \\ 2 & 2 & 1 \end{vmatrix} \\ =1.(-1).1+3.2.2+2.2.2 \\ \: \: \: -2.(-1).2-2.2.1-1.2.3 \\ =-1+12+8+4-4-6 \\ =13$

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