Tolong bantu jawab soal matriks tersebut

Berikut ini adalah pertanyaan dari iqbal03ip pada mata pelajaran Matematika untuk jenjang Sekolah Menengah Atas

Jawaban dan Penjelasan

Berikut ini adalah pilihan jawaban terbaik dari pertanyaan diatas.

Jawab:

Penjelasan dengan langkah-langkah:

Matrix 4 × 4

Menentukan Determinan

Diketahui :

$P_{4\times4}$ = $\left[\begin{array}{cccc}1&7&3&-9\\-4&6&-4&0\\0&-5&2&3\\-9&8&-1&-3\end{array}\right]$

Determinan

$\begin{aligned}&=1\times\begin{vmatrix}6&-4&0\\-5&2&3\\8&-1&-3\end{vmatrix}-(-4)\times\begin{vmatrix}7&3&-9\\-5&2&3\\8&-1&-3\end{vmatrix}\cdots\\&+0\times\begin{vmatrix}7&3&-9\\6&-4&0\\8&-1&-3\end{vmatrix}-(-9)\times\begin{vmatrix}7&3&-9\\6&-4&0\\-5&2&3\end{vmatrix}\\\\&\end{aligned}$

$\begin{aligned}&=\begin{vmatrix}6&-4&0\\-5&2&3\\8&-1&-3\end{vmatrix}+4\times\begin{vmatrix}7&3&-9\\-5&2&3\\8&-1&-3\end{vmatrix}\cdots\\&+0\times\begin{vmatrix}7&3&-9\\6&-4&0\\8&-1&-3\end{vmatrix}+9\times\begin{vmatrix}7&3&-9\\6&-4&0\\-5&2&3\end{vmatrix}\end{aligned}$

∵ cari per bagian bagian agar tidak bingung

Bagian 1

$=\begin{vmatrix}6&-4&0\\-5&2&3\\8&-1&-3\end{vmatrix}\\$

$=6\times\begin{vmatrix}2&3\\-1&-3\end{vmatrix}-(-4)\times\begin{vmatrix}-5&3\\8&-3\end{vmatrix}+0\times\begin{vmatrix}-5&2\\8&-1\end{vmatrix}$

$= 6\times (-3) +4\times(-9)+0$

= -18 + -36

= -54

Bagian 2

$= 4\times\begin{vmatrix}7&3&-9\\-5&2&3\\8&-1&-3\end{vmatrix}$

$= 4\times\begin{vmatrix}7&3&-9\\-5&2&3\\8&-1&-3\end{vmatrix}\begin{matrix}7&3\\-5&2\\8&-1\end{matrix}$

$= 4\times((7.2.-3)+(3.3.8)+(-9.-5.-1)-((8.-1.-3)+(-1.3.7)+(-3.-5.3))$

$= 4\times(105)$

= 420

Bagian 3

$=0\times\begin{vmatrix}7&3&-9\\6&-4&0\\8&-1&-3\end{vmatrix}$

= 0

Bagian 4

$= 9\times\begin{vmatrix}7&3&-9\\6&-4&0\\-5&2&3\end{vmatrix}$

$= 9\times\left(-6\times\begin{vmatrix}3&-9&\\2&3\end{vmatrix}+(-4)\times\begin{vmatrix}7&-9&\\-5&3\end{vmatrix}-0\begin{vmatrix}7&3\\-5&2\end{vmatrix}\:\right)$