Exercise Zone : Matriks [6]

Berikut ini adalah kumpulan soal mengenai matriks. Jika ingin bertanya soal, silahkan gabung ke grup Telegram, Signal, Discord, atau WhatsApp.

Tipe:

Standar SBMPTN HOTS

No.

Diketahui sistem persamaan linear dua variabel:
$\begin{aligned}2x-3y&=-4\\4x+2y&=8\end{aligned}$
Nilai $10x+10y$ adalah ....

$\begin{pmatrix}2&-3\\4&2\end{pmatrix}\begin{pmatrix}x\\y\end{pmatrix}=\begin{pmatrix}-4\\8\end{pmatrix}$

$\begin{aligned} D&=\det\begin{pmatrix}2&-3\\4&2\end{pmatrix}\\&=2\cdot2-(-3)\cdot4\\&=4+12\\&=16\end{aligned}$
$\begin{aligned} D_x&=\det\begin{pmatrix}-4&-3\\8&2\end{pmatrix}\\&=-4\cdot2-(-3)\cdot8\\&=-8+24\\&=16\end{aligned}$
$\begin{aligned} D_y&=\det\begin{pmatrix}2&-4\\4&8\end{pmatrix}\\&=2\cdot8-(-4)\cdot4\\&=16+16\\&=32\end{aligned}$
$\begin{aligned} x&=\dfrac{D_x}D\\&=\dfrac{16}{16}\\&=1\end{aligned}$
$\begin{aligned} y&=\dfrac{D_y}D\\&=\dfrac{32}{16}\\&=2\end{aligned}$
$\begin{aligned} 10x+10y&=10(1)+10(2)\\&=10+20\\&=30\end{aligned}$

Jadi, $10x+10y=30$.

No.

Jika matriks $\begin{pmatrix}3a&5\\-1&b\end{pmatrix} = \begin{pmatrix}9&5\\-1&a\end{pmatrix}$ maka tentukan nilai dari $2a+b$!

Latihan PAS Ganjil 2021

$\eqalign{ 3a&=9\\ a&=\dfrac93\\ &=3}$

$\eqalign{ b&=a\\ &=3 }$

$\eqalign{ 2a+b&=2(3)+3\\ &=6+3\\ &=\boxed{\boxed{9}} }$

Jadi, $2a+b=9$.

No.

Tentukan hasil perkalian matriks $\begin{pmatrix}2&-2\\2&3\end{pmatrix}\times\begin{pmatrix}2\\2\end{pmatrix}$!

SUMBER

$\eqalign{ \begin{pmatrix}2&-2\\2&3\end{pmatrix}\times\begin{pmatrix}2\\2\end{pmatrix}&=\begin{pmatrix}2\cdot2+(-2)\cdot2\\2\cdot2+3\cdot2\end{pmatrix}\\ &=\begin{pmatrix}4+(-4)\\4+6\end{pmatrix}\\ &=\boxed{\boxed{\begin{pmatrix}0\\10\end{pmatrix}}} }$

Jadi, $\begin{pmatrix}2&-2\\2&3\end{pmatrix}\times\begin{pmatrix}2\\2\end{pmatrix}=\begin{pmatrix}0\\10\end{pmatrix}$.

No.

Jika matriks $A=\begin{pmatrix}1&2\\2&1\end{pmatrix}$ dan $B=\begin{pmatrix}-1&3\\0&2\end{pmatrix}$ maka tentukan nilai dari $2A+B$!

Latihan PAS Ganjil 2021

$\eqalign{ 2A+B&=2\begin{pmatrix}1&2\\2&1\end{pmatrix}+\begin{pmatrix}-1&3\\0&2\end{pmatrix}\\ &=\begin{pmatrix}2&4\\4&2\end{pmatrix}+\begin{pmatrix}-1&3\\0&2\end{pmatrix}\\ &=\boxed{\boxed{\begin{pmatrix}1&7\\4&4\end{pmatrix}}} }$

Jadi, $2A+B=\begin{pmatrix}1&7\\4&4\end{pmatrix}$.