Exercise Zone : Matriks [4]

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.

Transpos dari matriks A=$$\left(\begin{array}{ccc}1& -2& 3\\ -4& 5& -6\end{array}\right)$$ adalah

A^{T}=$$\left(\begin{array}{cc}1& -4\\ -2& 5\\ 3& -6\end{array}\right)$$

Jadi, A^{T}=$$\left(\begin{array}{cc}1& -4\\ -2& 5\\ 3& -6\end{array}\right)$$.

No.

Determinan dari matriks $$\left(\begin{array}{ccc}2& -3& 4\\ -5& 6& -7\\ 8& -9& 10\end{array}\right)$$ adalah ....

$$\begin{array}{rl}det& =\left|\begin{array}{ccc}2& -3& 4\\ -5& 6& -7\\ 8& -9& 10\end{array}\right|\\ & =2\left|\begin{array}{cc}6& -7\\ -9& 10\end{array}\right|-(-3)\left|\begin{array}{cc}-5& -7\\ 8& 10\end{array}\right|+4\left|\begin{array}{cc}-5& 6\\ 8& -9\end{array}\right|\\ & =2(6\cdot 10-(-7)\cdot (-9))+3((-5)\cdot 10-(-7)\cdot 8)+4((-5)\cdot (-9)-6\cdot 8)\\ & =2(60-63)+3(-50+56)+4(45-48)\\ & =2(-3)+3(-6)+4(-3)\\ & =-6-18-12\\ & =\boxed{{\displaystyle \boxed{{\displaystyle -36}}}}\end{array}$$

Jadi, determinan dari matriks $$\left(\begin{array}{ccc}2& -3& 4\\ -5& 6& -7\\ 8& -9& 10\end{array}\right)$$ adalah -36

No.

Tentukan nilai a dan b jika $$\left(\begin{array}{cc}3a& 2\\ 6& -{\displaystyle \frac{1}{3}}b\end{array}\right)$$=$$\left(\begin{array}{cc}15& 2\\ 6& 7\end{array}\right)$$

SUMBER

$$\begin{array}{rl}3a& =15\\ a& ={\displaystyle \frac{15}{3}}\\ & =\boxed{{\displaystyle \boxed{{\displaystyle 5}}}}\end{array}$$

$$\begin{array}{rl}-{\displaystyle \frac{1}{3}}b& =7\\ b& =7\cdot (-3)\\ & =\boxed{{\displaystyle \boxed{{\displaystyle -21}}}}\end{array}$$

Jadi, a=5 dan b=-21.

No.

Tentukan hasil kali dari kedua matriks berikut.
$$\left(\begin{array}{cc}-1& -6\\ -5& -9\end{array}\right)$$$$\left(\begin{array}{c}3\\ -1\end{array}\right)$$

SUMBER

$$\begin{array}{rl}\left(\begin{array}{cc}-1& -6\\ -5& -9\end{array}\right)\left(\begin{array}{c}3\\ -1\end{array}\right)& =\left(\begin{array}{c}(-1)(3)+(-6)(-1)\\ (-5)(3)+(-9)(-1)\end{array}\right)\\ & =\left(\begin{array}{c}-3+6\\ -15+9\end{array}\right)\\ & =\boxed{{\displaystyle \boxed{{\displaystyle \left(\begin{array}{c}3\\ -6\end{array}\right)}}}}\end{array}$$

Jadi, $$\left(\begin{array}{cc}-1& -6\\ -5& -9\end{array}\right)$$$$\left(\begin{array}{c}3\\ -1\end{array}\right)$$=$$\left(\begin{array}{c}3\\ -6\end{array}\right)$$

No.

Tentukan hasil kali dari kedua matriks berikut.
-7$$\left(\begin{array}{c}6\\ 8\end{array}\right)$$$$\left(\begin{array}{cc}-5& 7\end{array}\right)$$

SUMBER

$$\begin{array}{rl}-7\left(\begin{array}{c}6\\ 8\end{array}\right)\left(\begin{array}{cc}-5& 7\end{array}\right)& =\left(\begin{array}{c}-42\\ -56\end{array}\right)\left(\begin{array}{cc}-5& 7\end{array}\right)\\ & =\left(\begin{array}{cc}(-42)(-5)& (-42)(7)\\ (-56)(-5)& (-56)(7)\end{array}\right)\\ & =\boxed{{\displaystyle \boxed{{\displaystyle \left(\begin{array}{cc}210& -294\\ 280& -392\end{array}\right)}}}}\end{array}$$

Jadi, -7$$\left(\begin{array}{c}6\\ 8\end{array}\right)$$$$\left(\begin{array}{cc}-5& 7\end{array}\right)$$=$$\left(\begin{array}{cc}210& -294\\ 280& -392\end{array}\right)$$.

No.

$$\left(\begin{array}{cc}7& 6\\ 6& 6\end{array}\right)$$\cdot$$\left(\begin{array}{cc}-2& 8\\ 6& -8\end{array}\right)$$= ,,,,

SUMBER

$$\begin{array}{rl}\left(\begin{array}{cc}7& 6\\ 6& 6\end{array}\right)\cdot \left(\begin{array}{cc}-2& 8\\ 6& -8\end{array}\right)& =\left(\begin{array}{cc}(7)(-2)+(6)(6)& (7)(8)+(6)(-8)\\ (6)(-2)+(6)(6)& (6)(8)+(6)(-8)\end{array}\right)\\ & =\left(\begin{array}{cc}(-14)+(36)& (56)+(-48)\\ (-12)+(36)& (48)+(-48)\end{array}\right)\\ & =\boxed{{\displaystyle \boxed{{\displaystyle \left(\begin{array}{cc}22& 8\\ 24& 0\end{array}\right)}}}}\end{array}$$

Jadi, $$\left(\begin{array}{cc}7& 6\\ 6& 6\end{array}\right)$$\cdot$$\left(\begin{array}{cc}-2& 8\\ 6& -8\end{array}\right)$$=$$\left(\begin{array}{cc}22& 8\\ 24& 0\end{array}\right)$$.

No.

Berikut ini adalah tabel banyaknya kendaraan dalam 2 hari.

	Senin	Selasa
Mobil	2	3
Motor	4	5

Tabel di atas dapat disajikan dalam bentuk matriks yaitu ....

SUMBER

$$\left(\begin{array}{cc}2& 3\\ 4& 5\end{array}\right)$$

Jadi, matriksnya adalah $$\left(\begin{array}{cc}2& 3\\ 4& 5\end{array}\right)$$

No.

Matriks berikut,
$$\left(\begin{array}{ccc}2& 3& 4\\ 5& 6& 7\end{array}\right)$$
mempunyai baris sebanyak ....

SUMBER

banyaknya baris matriks tersebut adalah 2.

Jadi, $$\left(\begin{array}{ccc}2& 3& 4\\ 5& 6& 7\end{array}\right)$$ mempunyai baris sebanyak 2.

No.

Matriks berikut,
$$\left(\begin{array}{ccc}2& 3& 4\\ 5& 6& 7\end{array}\right)$$
mempunyai kolom sebanyak ....

SUMBER

banyaknya kolom matriks tersebut adalah 3.

Jadi, $$\left(\begin{array}{ccc}2& 3& 4\\ 5& 6& 7\end{array}\right)$$ mempunyai kolom sebanyak 3.

No.

Matriks berikut,
$$\left(\begin{array}{ccc}2& 3& 4\\ 5& 6& 7\end{array}\right)$$
mempunyai ordo ....

SUMBER

banyaknya baris matriks tersebut adalah 2. Banyaknya kolom matriks tersebut adalah 3. Jadi ordonya adalah 2\times 3.

Jadi, ordonya adalah 2\times 3.